I had a fue tank like that - I had it steamed, then welded each pit. It was time comsuming, but got the job done. You can use TIG, MIG, or Stick Electrode. I would use 3/32", 6010. or 7018. If you have some leakers, there will be others almost ready to leak.
I assume that the tank is steel. What your seeing from the outside is the small end of a crater on the inside (I was thinking there was moisture on the inside, but you said outside. How thick is the material? Welding on a tank that has had petroleum products in it can be hazardous. There are ways to cure them. The ways that involve shortcuts, are dangerous. Taking it some where & haveing it steamed, is the best & safest all around. Then depending on how much experience you have welding, & the type of welder you have availiable, you can weld those spots up, just putting a spot of weld on it. Depending on how many you have, you can probably assume there are more on the inside.
Look inside after its cleaned. if it looks bad inside, have a piece of 16 guage formed that covers the bottom and up on the sides about an inch - weld it all around. Use a synthetic type of material between the bands. That won't harbor the moisture like cotton based straping does. Sorry this rambles.
Lee in Alaska