Can I paint over the tiles? If so what kind of products would I use and how would I prep the tiles?
You say it's for the 40's is the tile plastic?, if so get a wide 3-4'' metal scraper and pop all the tile off the first one may need a little elbow grease but once you get the first one the rest goes easily. The glue will still be on the wall so invest in a good heat gun and heat and scrape all the glue off the walls. These walls should be plaster so you shouldn't have a problem. What ever is left on the walls can be lightly sanded til smooth, wash walls, prime and paint. It will take some time but the end result is worth it. I did this in a 50's kitchen and bathroom, the tile in the tub was even on the ceiling. Good luck! If the tile is ceramic its a whole other story and project. Painting than would be advisable because you would ruin most of the walls removing ceramic tiles.
I wouldn't do it. You would either have to paint the grout, or put masking tape on the grout. Plus, as you point out, most paint won't stick to tile very well. There are some 2-part epoxy paints made for resurfacing sinks and tubs (white, almost always), but it's a fussy paint to work with, you need to prep the tile (sand it so it's not glossy), then mask the grout (probably). Edit: On 2nd thought, assuming the grout is white, you could also sand the tiles (for the paint to stick), and just paint using an oil-based primer. It will stick to the tile better than most paint. It might be a decent stop-gap until you have time to re-tile.
i wouldn't paint them . . .I used to have this shower remodel job for a college, we'd have to paint over the old shower tiles with the above mentioned 2-part epoxy paint...and it sucked. not only was it a hassle to sand those tiles, but to mix the paint and get it smooth and even...it's just very frustrating and i wouldn't wish it on my enemies. if the tiles are REAL BAD, then save up and just do a bathroom remodel...if not, then use other colors to accent the bathroom. blue and yellow go well togther, also blue and orange...or you could get a rich brown to go with it, it really depends on the blue and how bad it is. hope this helps good luck