This looks like an interesting project. The burn mark looks too deep to remove without replacing the veneer. The bubble is straightforward. With a razor, slice the veneer with the grain the full length of the bubble and with a syringe apply glue under the entire bubble. But before doing these repairs the table should be fully stripped and the wood cleaned. What did you use to strip it? Sometimes this takes many applications. If the piece can be disassembled easily, it should be done. Check all glue joints to see if any are loose or can be loosened. If the glue joints are all tight, leave them, but stripper sometimes loosens them. Depending on where you are in the process and what chemicals you've already used, will determine what steps to do next. You'll need to have a number of solvents on hand, but you should post the details of what you've already done before going on.

Sanding frees the lead into the dust---NOT GOOD. Stripping keeps the paint damp and cohesive---GOOD. (Unless the resulting goop dries out.) I can say fairly positively that wood is not poplar(poplar is listed as a hardwood---but is relatively soft and does not wear well under use.) I should have been more precise. The back woods do indeed look like pine, but the drawer fronts are mahoghany, IMHO. Mahoghany cut over 50 years ago(Old growth) had a much more dense grain than modern stuff(New growth).

I don't really have a solution on hand for you. But there are several lessons here: 1. Oil has virtually no protection against moisture. In fact some oils are hygroscopic (meaning they have less than 0 water resistance, actually attracting moisture). 2. Wax has virtually no protection against moisture. As one finishing expert writes, "Wax is the closest thing to no finish at all." .3. Don't believe everything you read on the internet. OxiClean is sodium percarbonate, that when mixed with water, has a chemical reaction that creates hydrogen peroxide. That is a bleaching agent and why it works on things like clothes. When you are using a new product or process, ALWAYS test out on a piece of scrap of the same material or in an obscure spot. 5. Wood bleaches are not "spot cleaners." Most are designed to be used over a whole piece, and on raw wood. http://www.woodcentral.com/bparticles/woodbleach.shtml Like I said, I don't have a good answer for you. Oaks are tannin-rich wood. Chemical reactions between tannin and iron can create black spots like this. Might there be iron in your tap water? The article above talks about oxalic acid as a way to remove this, with all the above warnings on its use. I'd be tempted to just leave it and not make anything worse.

Old English furniture polish (which this is) lists this product as an oil. It is possible/probable that you can leave it alone and the oil will eventually disappear with normal cleaning methods (hardwood floor cleaner such as Bona, Loba, Polywhey Cleaner, etc). Even a 'drop of dawn' soap in 1 gallon of water would do it. As mentioned above, a bit of bleach (5% solution on wood is about as exciting as you want to get) *might do it. If I'm correct and this is a temporary 'oil' then a mild degreaser (such as Windex original) can get rid of this stuff. I would be VERY cautious when using ANYTHING other than a wood floor cleaner. Personally I would dampen a clean cloth with the Windex and then LIGHTLY DAB at a bit of the dark colour. I would check the clean cloth to see if there is any 'old english' that is coming up. If it is, I would continue to be very gentle with the removal. And for the record, these 'oil' based products can cause damage to wood floors to the point where they may not be refinished in the future. That would be a TERRIBLE upset to someone who just wanted to make their floors look 'a little better'. You currently have a CLEAR finish over the wood. To get rid of the LOOK of nasty scratches (from dragging things across the floor), you can work with a FINISH pen. Yep. Home Depot, etc carries many versions of Finish pens. These are pen-like containers filled with URETHANE. You use them like a stain-pen...except there is zero colour. All you have to do is match the gloss level of your floor and voila you have a 'cure' for damaged finish. And the good thing about finish-pens is: they do NOT damage the wood nor cause any issues with future refnishing. Anything 'oil' (ahem...Murphy's Oil Soap, oil soap of any kind, 'eco' cleaners of any kind, etc, etc, etc) can and will contaminate the WOOD underneath to the point that future refinishing *could be made impossible.