None of those fish belong in a ten gallon. I'm going to say there's too many fish, creating too much waste, perhaps in an uncycled tank, and the build up of waste products is killing them. Might want to check out the Nitrogen Cycle.
For one angel, I say a 30 gallon is the minimum. No idea what kind of fish the "white cichlids" are, but if they're not kribensis or shell dwelling (both are small species) they will probably need at least a 30 as well.
If you can, I say get a 55 gallon set up and move all the fish into it. The tetras will get eaten by the cichlids once they get big enough, and they prefer to be in large schools anyways. Consider rehoming them.
If you can't get a 55, rehome the angel and cichlids, up the neons to 7 or so, and call it good. Honestly, very few fish can live happily in a 10 gallon, it's just too small. I personally wouldn't keep any tetras in a 10 because they are so active and love their swimming room.