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Testing for Java SDK

I am writing an application in Java. Does a Java SDK have to be installed to run the application from the command line? If so, can I package the SDK with the application to be installed when installing the application?

From Java 9 onwards you can use jlink to produce a custom JRE for your application. The JRE includes a copy of the java command and (only) the libraries / classes that your application needs. It will be platform specific.
From Java 14 onwards, you can use jpackage to produce (platform specific) native executables for Java applications.
There are also 3rd-party tools that can generate executables, and third party installer generators that (in some cases) can install Java for the end user.
Note: if you take the approach of distributing your application as a self-contained JRE or native executable, the user no longer has the option of updating their Java to address security related issues. It becomes your problem / responsibility ... as the supplier of the software ... to make available in a timely fashion application updates that incorporate the new Java releases with important security patches.

If you use something like GraalVM to compile a native binary, then there is nothing more you should need for a simple application (meaning, nothing is tried to dynamically load classes at runtime with reflection)
Other than that, the Java JRE is required, and can be included as part of an application package; for example, IntelliJ or Eclipse IDE come with their own JRE.

Thanks everyone for your input.
After doing more research I found that by using a jdk greater than 8.?, it is possible to bundle everything an application needs in the deployment process.

What packaging tool should I use for a Mac/Windows Java app?

I have a Java desktop app that runs on both the MacOS and Windows.
I understand that I cannot have one distribution for each, which is not a requirement.
I need to know what tool or tools is best to use when delivering a Java app for each.
The tool should install prerequisites (in this case, Java and some JARs) and look native to the respective operating system.

As for OS X's java situation:
Currently, JDK 6 is bundled in the OS.
Presumably, the next version of the OS will still include JDK 6.
It's publicly stated that the OS will have a well-defined place to install multiple copies of Java runtimes, a public interface choosing which of the Java version, etc. See here.
Apple started contributing back its own code to the open JDK community, so JDK 7 should be available as a separate download, see here.　
So, you're not expected to include Java runtime itself into your Java app even then. You're not supposed to install Java in a ramdom place on a filesystem, for example.
As for how you should deploy java apps on OS X:
Double-clicking jar just works.
However, that won't be pretty, because you would only have a generic Java icon in the Dock. You don't want that.
You should use Jar Bundler to make it an honest OS X app. On Mac, it comes with XCode. See the documentation here. You can do that on a non-Mac machine too, using this open-source project.

On Windows, I would recommend either JSmooth or WinRun4J.
On a Mac, the situation is a bit more complex (as the comments point out), but just distributing an executable JAR is probably good enough for now.

How to do a professional setup for java app to avoid "javaw" cannot be found?

I just installed http://yacy.net/
It advertises as easy install except that when I run it says cannot find javaw which spoils nearly everything.
If I were to distribute a java app myself I'd like not to have user knows anything about downloading and installing java, so any article, tool which explains how to package a java app professionally like one can do with a windows app easily ?

There are several approaches to this, all of which have their own set of drawbacks. Here are some of the most popular:
Bundle a private JRE with your application. See the README file that comes with your JRE for the details.
Use a launcher (such as launch4j) that can download a JRE at runtime if a suitable one is not found on the target machine.
Compile Java to native, then distribute as a regular Win32/Linux executable. You can do this with Excelsior JET.
Since you are concerned with deployment, you'll probably also want to create an installer for your application. There are dozens of options for this, such as NSIS.

What is the best way of packaging Java software for running on Windows?

What's the best way to package Java software for running on Windows? Is there a standard for writing .BAT files which can discover the latest installed JRE on the machine? Are there any Maven plugins for this? What's the deal with executable Jar files?

I would without any doubt recommand you to use Java Web Start, as it allows you easy control over version used (and by far the easier to use update mechanism available nowadays).

Depends on what you need.
We've found that using the One-JAR + JSmooth gives a very good user experience as it allows us to distribute a single EXE-file which can be put anywhere on the users system, as opposed to having installation binaries, which need to be installed and uninstalled etc. etc. etc. JSMooth checks for the existance of the appropriate Java runtime, and redirects to the official download site if none is found.
The reason for One-jar is that you generally need to use library jars which is best to have separately but JSmooth only allows for a single jar file.
Also the One-Jar SDK and JSmooth is scriptable without being tied to Windows, so we can build new versions on our Hudson engine running on Linux.

In the past I've used a java installer package like launchForJ. However, a lot of these packages use Java so you may need to a batch or simple executable written in native windows code that does a quick check to see if Java is already installed then run the installer.
Since Java uses system variables during install you should be able to check if the version (or higher) that you require exists in this way.

The standard way would be to use Java Web Start.
Using Java Web Start technology, standalone Java software applications can be deployed with a single click over the network. Java Web Start ensures the most current version of the application will be deployed, as well as the correct version of the Java Runtime Environment (JRE)
Maven has a Webstart Maven Plugin to help building application bundles that can be deployed via Web Start.
An alternative solution would be to use a cross-platform installer generator to generate, well, an installer. I personally like IzPack (I think that JSmooth is very similar but I have more experience with IzPack) and, if you are specifically targeting the Windows platform, you could use IzPack to Build [a] Native Windows Installers with IzPack Native Launcher:
A problem still arise with IzPack when
the target system does not have a JRE
installed. The user needs to first
install it and then run the IzPack
installer. This is not a problem with
Linux or BSD users since they are
generally skilled and they know how to
do that by hand or with a packaging
system (RPM, DEB, ebuilds, ports,
...). Similarly, a Mac OS X user will
not have much problems since it is
available with the operating system.
However the situation is more
complicated on the Windows platform as
a JRE must be installed. Worse,
several instances can be installed in
a sometimes messy situation.
The IzPack Native Launcher tries to
solve this problem. It is a C++ native
application that is available under
the very permissive MIT License and
that uses wxWidgets for the GUI. It is
thus cross-platform (for the
historians: it was first developed on
a FreeBSD box), but most people will
need it on Windows. It uses a simple
configuration file and will first
check for a JRE. If none can be found,
it will pop-up a dialog to let the
user choose between the following
options:
manually specify a JRE location
download one from the Internet
install one that is provided by the packager (if available).
IzPack also offers a Maven Plugin. Worth the check.

JAR installer that auto-detects if Java is there and autostarts the application

I need to build an installer that does the following:
Installs my jar on the client.
Auto-detects if JRE is installed (in which case it does not re-install it), otherwise installs it without the user clicking on another button.
Auto-starts the application when the client is booted.
Works across Windows, Mac and Linux.
Any idea how to go about it?

If a commercial tool is ok, I can recommend install4j. 1, 2 and 4 are easy to do with it, but about 3 I'm not sure. Edit: You could probably achieve that by installing your app as a "service", which install4j supports for all platforms. Quoting from its Features page:
install4j offers full support for
generating and installing services
(daemons). For services, install4j
generates service executables on
Windows, startup items on Mac OS X and
start/stop scripts on Unix/Linux
platforms.
Edit: Regarding #2, JRE detection: install4 has pretty nice, flexible options for JRE bundling/detecting. You can include a JRE (statically or dynamically, shared or not) or prefer to use one already present, with the possibility to download a JRE from within your installer as a fallback. Check these docs for more: How Installers Find a JRE and JRE Bundles.
(More about my experiences with install4j.)
For other tools, you could check some of the earlier Java installer questions on SO:
What’s the best way to distribute Java applications?
Java Application Installers
What is the best installation tool for java?

Commercial tools like InstallAnywhere can do that. After installing the JAR (and links and such), installers can check the registry if Java is already installed and proceed or not. As long as the installer supports all needed plattforms, you are fine.

You could use launch4j , it does not automatically install java however. But maybe there's a way to make that work by packaging the JRE for example.

You may also want to take a look at BitRock InstallBuilder, it provides built-in functionality to perform what you want. We will be happy to build a sample installer for you, just drop us a line.

I recommend downloading the source code for the build scripts of popular Java programs like limewire and follow their example. The end.
...Or you can do like I did:
I have done the JRE detection and
download/install of redistributable if required with
NSIS on Windows. Maybe an .msi is better than a installer.exe which NSIS creates. I believe msi are more like packages on mac so they allow proper updates. Maybe NSIS creates MSIs... not sure.
Mac is simply an Java App
bundle and you specify the JRE and other Java info in the
info.plist and you can optionally create a .pkg
file to give the user an installer and bundle up in a dmg using the command line dmg programs.
I haven't done Linux and don't plan to... sorry :)
All this was a fair chunk of work. I first did the Windows stuff then a couple years later did the Mac stuff.
You can integrate all of this in NSIS build scripts and Ant. I can't remember why I didn't use install4j. Probably I was too cheap :)

Haven't heard of anything that works across all those platforms, but JSmooth might help (fits your needs on Windows). I've used it about 2 years ago and it worked fine.