Mineral Spirits Vs Acetone
Use lacquer thinner for oil. Most lacquer thinner contains a lot of acetone. You could use straight acetone too (which is the same formulation as nail polish remover). It will eventually dissolve plastic brush handles.
If I intend to use the brush (or roller) again soon and with the same color, I wrap them in saran wrap or a plastic bag and stick them in the fridge.