Stomp version 1.19+ supports a limited set of commands through AppleScript - enough to setup destination folders ask Stomp to perform compression tasks using various presets.
Note that the same limitations of Stomp apply from within AppleScript. The primary one being that you cannot ask Stomp to compress one file using multiple presets (the same is true in the UI at the time of writing). You can however ask Stomp to compress one file many times using different presets.
Here's an example, showing me setting up the destination folder to Stomp Output on my desktop, and then compressing a test file (aaa.mov) using H264. The final "remove from recordings upon completion" ensures that Stomp removes the recording when it's done. It removes it from it's internal list (the same list you see at the bottom of the window).
Best explained with a video, but first, the script:
tell application "Stomp"
activate
set destinationFolder to "/Users/neil/Desktop/Stomp"
compress file "/Users/neil/Desktop/aaa.mov" preset name "H264" with remove from recordings upon completion
end tell
Example of driving Stomp via AppleScript