Is it possible to remove tokens from dead projects/tokens that are totally useless and worth $0 from my wallet? Do I just send them to a random address? I don't want to burden anyone else with those shitcoins 
Why does it matter? It will do no harm. You can send it to any random wallet but you'll be needing some gas.
It doesn't make sense. If you want a clean wallet then just go create a new one. Tokens cannot be deleted like anything in the blockchain, it is made to be that way.