I like and use the free Audacity program. I also now use a Tascam DP-004 multi-track recorder, but before I had it, I just used Audacity to lay down multiple tracks. If you are a Mac user, there are free tools there too.
I have an old version 6 of Sony Vegas, which works just fine for doing those multiple split screens. I believe some of the inexpensive versions of Sony Vegas do the same thing, but i have not used them.
Are you just wanting to do split screens and multi track audio video?
If so power director will do that. Here is a quick and not so great first try at that with free trial version. I recently bought the full version and hope to get better at it.