A shitvite is short for "shitty invite", an invite to do something you don't want to do. It can be an invite under false pretense or a trick to have you do something you normally wouldn't do.
I got a shitvite from Tom this weekend.. He invited me over to help him move out of his apartment .
A Shitvitation is when you are invited to a friend's place and you take a massive shit in their bathroom and then proceed to leave immediately after.
Dude came over and used my bathroom like I gave him a Shitvitation.