I use a product which is basically identical to twin air filter solvent. It is good since you can use it like a parts cleaner too. I get all the dirt out by submersing the filter and then letting the liquid run from the inside out. This flushes all the dirt away in about two minutes. Then I get the garden hose and lightly spray the filter from inside out and when I don't see any solvent anymore, looks white, I know it is time to wring it out gently and hang to dry.
I read in a magazine that Belray foam filter oil was best since it is thick when it comes out of the bottle. It does keep a lot more oil in your filter and if you are not good at getting rid of the excess oil it can cause a rich condition in the carb. I also tried silkolene and it is very watery and is much more easily applied. I use a pan and pour some over the filter and then mop the oil up with the filter and press down on the filter to ensure even coverage. Then once that is done I squeeze it all in my hand to get rid of excess oil. The excess is easily poured back into the bottle from the pan.
Store your freshly oiled filter in a big freezer bag. I position the filter in a corner with the bottom or seam of the filter at the bottom, toward the corner. Then I seal the bag with as much air in it as possible. This keeps the filter from resting too much on the plastic of the bag. Why do this. When I store the filter in the bag, it is hung by a corner so the corner beneath the filter is able to catch all the remaining excess oil and when you go to take the filter out of the bag, this oil is not reintroduced to the filter.
Whew, that was a long explanaition.
I like both oils, silk for wet and bel for dry conditions.