I just finished putting a new floor and firewall in my '40 Ford. What are people using to seal the seams inside and out?

Most will use auto body seam sealer. Should be able to get it just about anywhere, you can get a tube that fits in a caulking gun.
Mastic tape is also good stuff- I may or may not have used mastic tape to fix a tiny crack in a weld on an oil pan sump between rounds. It worked like a champ!

I recently sealed the tubs to body on my race car with 3M 08367 seam sealer from NAPA using a caulk gun. This is the first time I ever used a product like this and think it did a good job imho.