How to fix sheet metal holes?

The most effective and permanent way without welding is. Take small pieces of flat metal and after cleaning the back of the hole on the panel. glue them to the back using JB weld quick set, After they dry fill the hole from the outside with the same and cut them flush with a razor blade while still soft. Works pretty good. Once they are cured you won't hit them off. Primer and paint right over them. You just have to make sure the metal on the panel is clean where you are gluing the little pieces to. I just closed up emblem holes in a hood for a guy that way. No warpage
This is an excellent idea!
I have a hood that is mint other than someone decided to mount twin scoops ('70 Swinger style) onto it and in the wrong place to boot...........
I think I'll try your tip to save this hood.

To the O.P., DO NOT braze the holes shut (with brass rod using an oxy and acetylene torch I take it) , the warpage would be incredible as well as paint and bondo won't stick to brass in the long term.
They used to use this method in the '50s to '70s before mig welders became popular.
I've heard of people soldering or leading the holes shut, but I have my doubts on how long it would last being dissimilar metals and all.

Whatever method you decide on, it has to be clean, clean, clean before you do it!

Heat is your enemy here, and I'm thinking the technique that OMM says is the safest and most durable.
J.B. weld is some strong ****!