Mineral Spirits Vs Acetone

It really depends on what your 'oil' paint actually is using for its carrier which forms into the film, as well as the solvent.
Not many true long oils still used in 'house paints'. Linseed oil was and still is the most common, but I've seen other animal and vegtible oils on the labels over the years.
Even those that still contain long oils, also have modified oils - alkyds, and with varnishes and enamals, often resins as well for hardness.
Most common now in VOC limited areas are alkyds and urethanes.
All the above should clean up with mineral spirits or paint thinner. The problem with the new VOC alkyds and urethanes etc is they set up quicker. There's less time to lay them onto the wood, and less time exposed to air before they start to set up.
If its not too bad, the hanging method shown above is helpful. They still need to be spun out as much as possible until there's nothing coming out. You can spin by hand - a spinner is just convenient. Sometimes you have to work some out by hand or with a metal comb. I try not to let it get that bad. Its quicker overall to stop and clean the brush before that happens.

All the above assumes using a real bristle brush, and not working with epoxy other specialty or industrial coatings.
If a high percentage of resins have been included in the paint, and they have started to set up - something stronger - like paint remover or brush cleaner may be needed. It also may ruin the brush.
There are some new soap and water clean up 'oil paints'. I don't trust 'em so no observations on them.
Also any paint that forms a film from an emulsion in water (commonly all called latex, but mostly acrylic now) is a different animal entirely. Once those start to set up, it takes something strong to completely break them down. With 'latex', the right brush is a synthetic brush, often nylon. Using the wrong brush for the paint just makes everything more difficult including cleanup.

PS. Mineral spirits can be reused again and again. Let the pigment settle tothe bottom, then pour off the spirits. Let the pigment dry out and its safe to dispose.