So I have this yamaha pitbike and I know I should always clean my air filter each ride.

I have a spair air filter and it's a UNI filter, in kind of sponge stuff.

I have a air filter cleaner and a dust catcher, but on the can it says it's mainly for paper filters.

My question is : Can I use this dust catcher on a foam/sponge filter.

Also my way of cleaning it is I clean it with the cleaner and soft water, than once it's dry I put it in a oily stuff, kinda like kerosene or diesel, to keep it oily. Once it's dry I shoot this dust catcher ?

With a UNI filter just used the provided air filter oil it comes with and you should be fine. Make sure not to go over board with that shit a little bit goes a long way.

It came in a bag with no filter oil with it, otherwise I would use it.

You should be using foam filter oil. Bel ray and pj1 are my favorites.