How do I check if the Java JDK is installed on Mac?

javac -version in a terminal will do

You can leverage the java_home helper binary on OS X for what you're looking for.

To list all versions of installed JDK:

$ /usr/libexec/java_home -V
Matching Java Virtual Machines (2):
    1.8.0_51, x86_64:   "Java SE 8" /Library/Java/JavaVirtualMachines/jdk1.8.0_51.jdk/Contents/Home
    1.7.0_79, x86_64:   "Java SE 7" /Library/Java/JavaVirtualMachines/jdk1.7.0_79.jdk/Contents/Home

To request the JAVA_HOME path of a specific JDK version, you can do:

$ /usr/libexec/java_home -v 1.7
/Library/Java/JavaVirtualMachines/jdk1.7.0_79.jdk/Contents/Home

$ /usr/libexec/java_home -v 1.8
/Library/Java/JavaVirtualMachines/jdk1.8.0_51.jdk/Contents/Home

You could take advantage of the above commands in your script like this:

REQUESTED_JAVA_VERSION="1.7"
if POSSIBLE_JAVA_HOME="$(/usr/libexec/java_home -v $REQUESTED_JAVA_VERSION 2>/dev/null)"; then
    # Do this if you want to export JAVA_HOME
    export JAVA_HOME="$POSSIBLE_JAVA_HOME"
    echo "Java SDK is installed"
else
    echo "Did not find any installed JDK for version $REQUESTED_JAVA_VERSION"
fi

You might be able to do if-else and check for multiple different versions of java as well.

If you prefer XML output, java_home also has a -X option to output in XML.

$ /usr/libexec/java_home --help
Usage: java_home [options...]
    Returns the path to a Java home directory from the current user's settings.

Options:
    [-v/--version   <version>]       Filter Java versions in the "JVMVersion" form 1.X(+ or *).
    [-a/--arch      <architecture>]  Filter JVMs matching architecture (i386, x86_64, etc).
    [-d/--datamodel <datamodel>]     Filter JVMs capable of -d32 or -d64
    [-t/--task      <task>]          Use the JVM list for a specific task (Applets, WebStart, BundledApp, JNI, or CommandLine)
    [-F/--failfast]                  Fail when filters return no JVMs, do not continue with default.
    [   --exec      <command> ...]   Execute the $JAVA_HOME/bin/<command> with the remaining arguments.
    [-R/--request]                   Request installation of a Java Runtime if not installed.
    [-X/--xml]                       Print full JVM list and additional data as XML plist.
    [-V/--verbose]                   Print full JVM list with architectures.
    [-h/--help]                      This usage information.