Good question on the oil stains. Glenn probably has some better ideas. I would try wood bleach. Trisodium Phosphate.
You can find it in hardware stores in the paint section IIRC.
Rodney

Oil stains are hard to get rid of. Wood bleach will not help. Use corn starch by piling it up on the oil stains and let it set for a week or more. We have to try to get the oil out of the wood. If the starch turns dark change it and start over. Then hope for the best. Last resort is to stain the wood the same color as the oil stain that is left.

What I worry about most is getting a good finish over the oil. The stains I have after sanding I'm going to leave. Like I said this table is most likely older than I am so I think it just adds to the charactor a little. What don't to do is splatter on the table after I get it finished that stains it worse. The table can't help the stains it already has, but any more will be my fault. I'm thinking of a clear poly sanded between coats and maybe 3 or more coats. After a final sanding O would polish it out with a good grade auto wax. Does this sound like a plan that would work for a machine in metal shop where almost anything could happen.

Poly is a good choice but would not use poly. I would use a good oil based varnish. Only because it is easier to repair. Poly is not easy to repair.

Thanks Glenn. I guess varnish it will be.

I have never posted before so hope this is correct...this thread is wonderful! I am hoping to bring my Mom's 1955 Singer sewing machine cabinet (Style 42) back to life...unfortunately, it fell victim to a 1970s "antiquing kit in a box". I am assuming that I will need to strip this finish off before I can even begin to determine what TLC the cabinet should receive. What is the best product to remove the "kit in a box" finish? You help is greatly appreciated!

Oh, boy, kukla. My mom did the "antiquing kit in a box" thing on a table that had been my grandmother's. She later took it off but I can't remember what she used. The good news is that almost all of it came off without damaging the wood. I still have that table :)

The best way to remove the antique in a box is with a strong stripper. You can get a stripper at Lowes or Home Depot. Use gloves with the stripper. Any stripper will do but the citrus stuff is not the best.

Thanks to the info on this board, the cabinet has been stripped. Should I sand before applying stain since there is some "splotchiness" where the original stain is in the grain? I plan to use General Finishes vintage cherry.

Yes I would lightly sand the cabinet with 120 grit.