...without refinishing the floor or damaging the finish (much).
You will need: a steam cleaner, bamboo skewers (like the ones you use for kebabs), disposable wooden chopsticks, rags, rubbing alcohol, sponges with softish plastic scrubbers, toothbrushes, dish soap, buckets, warm water, cotton balls or pads.
Mop up any big spills while they are still wet. Hit remaining streaks, drips, and splotches with the steamer. Pour a little rubbing alcohol onto the stain, the rub it with a cotton pad until the paint starts to dissolve. Use the sponge to mop up the paint as it comes up, otherwise you'll just spread the old paint around on the floor. If the paint doesn't soften, hit it with more steam and alcohol, then try the toothbrush. If that doesn't work, try pushing gently at the edges with the chopsticks (don't break them in half; use the blunt side).
For paint that has seeped into grooves between the floorboards (a problem on pre-finished wood floors, which we have upstairs because they were brand new when we bought the house and we thought it would be wasteful to remove them - another story), use the pointy tips of the bamboo skewers to push the paint out.
We did this all last week, with lots of help from friends and family. Each room took ten hours.
There's still paint in the hallway and in a few places downstairs, but we're getting there.
Incidentally, we would have simply refinished the floors and sent the bill to the insurance company, but we didn't have time -- the vandalism happened six days before we were going to move, and the lease on our rental apartment was up.
Six days to repaint and clean the floors -- plus we still had to complete two bathrooms and finish installing the kitchen cabinets. Six days.
Everyone pulled together, and with a lot of help from friends, family, and our wonderful builder Bruce Eddy, we did it.