I still use oil-based enamels for everything I don't paint with automotive paint.
Like GeeBee, I use cellulose thinners with them. I tried white spirit and turpentine, but nothing works as good as cellulose.
I always carefully nick the little glass jam jars from the breakfast buffet in hotels. I fill three of them with cellulose.
The first is the 'dirty' one. This is where I stump in the brushes straight after I used them. After I wiped them on a cloth, I then stump them into glass no.2 and after another wiping they go into glass no.3 for a final rinse. Once glass no.3 is slightly contaminated, I dump what is in glass no.1, fill it with what's in glass no.2, fill glass no.2 with the slightly contaminated content of glass no.3 and fill glass no.3 with fresh cellulose.