This band is relatively new to me (although I have known about them for some time). I Picked up their album Sing To God out of pure curiosity. I have never listened to an album so many times in such a short amount as I have with Sing To God, it really is quite the unique experience and would encourage everyone to at least give it a listen.
Cardiacs music is noted as a balance of the raw energy of punk music, all the while adding the technical aspects of prog. They have established their own sound very well and essentially created their own genre known as 'pronk' (although Tim Smith seems to reject the term). But that's not the end of the list of genres they borrow influences, not gonna go all into detail about that but you get the idea. The music magazine Organ once commented saying that "one Cardiacs song contains more ideas than most other musicians' entire careers."