It got this way because of woodworking

I have never tried it on concrete, and it’s not magic, but Bix stripper will work on all the materials you mention. The other option is having your floor ground or sandblasted by a professional.

-- Wish I were Norm's Nephew

A friend of mine who owns an auto repair business had a similar situation….he had his professionally done…but a DIY could probably find the equipment at a good rental facility. First the guy ran a machine that uses hard plastic balls to pulverize the floor and remove the old paint and oil (very similar to a sandblaster…but using larger “sand”). I recall this machine looked like a large carpet cleaner. After cleaning, they put on a concrete etch and a layer of primer (they used a commercial spray gun…here again an item could be rented). Then they laid down a epoxy coating. The commercial guys used a machine that painted and applied heat to cure the floor very quickly as the shop could not be completely shut down for two days…even on the weekend….this could be done by roller or hand and given the time to cure/dry would take a few days or so. Of course in your situation you probably could use a concrete deck paint without all the hard core preparation since you don’t have as much oil and solvents as an auto shop does. I have to say though that the commercial application was extremely durable and very smooth – I would love to do this to my shop…and I possibly will in the future.

-- Woodworking.....My small slice of heaven!

Is it fresh or cured (the stain, etc)?

Is the floor concrete? If it is, and well aged, nothing beats sandblasting for cleaning concrete. It’s hard to rent a sandblaster (I tried once, plus it takes a trailer-sized compressor), but the work can be hired out.

Edit: a day late and a dollar short – again!

-- My broker promised me he would treat my money as if it were his own. Trouble is, he did.

I assume by your post that your concrete floor is not a glass smooth surface and that the surface has some degree of texture which prohibits simple scraping off of the floor. So I would use a chemical stripper on the spots needed and get as much up as possible. Then take a right angle grinder and attach a twisted wire cup brush to remove the rest of the paint from the floor. What won’t come up then should be prepped well enough to use epoxy paint to finish the floor.

-- I don't make mistakes, I have great learning lessons, Greg

Muriatic acid is commonly used for cleaning concrete when nothing else does the job. I’ve never used it, but as I understand you can get it at paint supply stores. Just be careful and be sure to follow all the safety instructions.

I am sometimes disturbed by the crap on my shop floor, but quickly get over it and go back to work.
I have done so much painting and greasy mechanical work over the years, I find it hopeless to worry about it.

I do wish for a seperate area for the dirty work though.

-- She thought I hung the moon--now she just thinks I did it wrong

id say go with muriatic acid and possibly rent a floor scarifier, we use one for demolition work when we have to grind off old floor carpet mastic

-- "there aren’t many hand tools as awe-inspiring as the #8 jointer. I mean, it just reeks of cast iron heft and hubris" - Smitty

Muriatic acid should work but it has very strong fumes make sure you have good ventilation and a means to flush it with water.

-- W James Brokenbourgh Custom furniture maker http://artisticwoodstudio.com/

I don’t know how to tell you to get it up, but I have a suggestion for everyone for future spills and drips.
I’m clumsy. I spill stain and paint all the time. The paint, once it dries, usually comes right up. The stain though soaks into my concrete floor, discoloring it forever. I keep my fine sawdust, like from my scroll saw or table saw, in buckets. If you throw a handfull of fine sawdust on stain drips, and a lot more sawdust on spills, it’ll soak it up without permanantly staingin your concrete. The only stains on my concrete floors now are the one’s put there before I realized this.

-- http://wddsrfinewoodworks.blogspot.com/

How are you going to finish the floor? If you’re going to paint it, just paint over it. Try a couple of paints to make sure it dosn’t bleed through.

-- Bruce from Central New York...now, if you'll pardon me, I have some sawdust to make.