I want to try this game without making/buying a board and it is easier to learn to play when the computer can prevent invalid moves. Does any software, preferably freeware, exist which simulates this flavor of chess?
There is software for playing Tri-D Chess; Parmen is a Windows application written by Doug Keenan and available free on his website.
Here are some of the external links for (software) Raumschach and Tri-D chess:
There is a version available for Android: https://play.google.com/store/apps/details?id=awfsoft.app.TriDChess