Water seeping up through bathroom tiles
Well stopping the leak would be your first priority. No clue on helping you find it. A toilet seal is not a hard job to tackle. Get a new wax ring and I'd suggest the extra thick version. Shut the water supply off and flush to get rid of as much of the tank water as possible. I use a wet/dry vac to remove the rest of the water. Remove the water supply line to the toilet and the remove the nuts on the 2 closet bolts holding the toilet to the floor. Once uninstalled, you need to scrap all of the old wax off the flange in the floor and the bottom of the toilet. Put the new seal over the flange and reseat the toilet on top, lining up the closet bolts to the holes in the toilet. Use some pressure down on the toilet to seat it. Tighten the nuts to the closet bolts BUT DON'T OVER-TIGHTEN. You can crack the toilet base, the toilet flange or pull the closet bolts out of their slots if you tighten too much. Hook the supply line back up and turn the water back on.
Now, having said that, when you mix water and wood, good things don't happen. First of all, mold is soon to follow. Secondly, wet wood can easily be damaged. I have no idea what you're going to find once you remove the toilet. Hopefully the wood around the flange isn't rotted! That will be a problem.
I think you need to determine where the leak is. Perhaps try to not use the toilet for a few days (if possible) to see if the floor starts drying out. Doubtful if the sink is leaking. You would be able to see water dripping from the drain or supply lines. Is there a tub or shower in this room? That could be a culprit.
Short term, you need to stop the leak and then try to air the room out. If you have a dehumidifier, that would be ideal. Try to get some air flow going, otherwise mold will be moving in shortly.