Your tetras might not be fine for two weeks without food, that's really pushing it. One week probably, two weeks, a whole lot less likely. The same thing applies to your betta.
The size of the fish and how well you've been taking care of them prior to leaving for vacation matters too. Bigger/older fish can go longer without food than smaller/younger fish. A full grown neon (~2 inches) can go longer without food than an immature neon. Have you been feeding them consistently, and changing their water at least once a week? Do you have live plants and a little bit of algae growing in your tanks? Neons will nibble on algae, so that can help keep them from starving to death, but algae won't feed them properly in the long term. Bettas don't nibble on algae.
For two weeks, you can try either those food blocks that slowly dissolve over time, or the automatic food dispensers. If you try a food block, test one out for a few days to make sure you fish will actually eat the dissolving food. The problem with dissolving food blocks is that they are continuously dissolving so they degrade your water quality. That effect is more pronounced in smaller tanks. Automatic food dispensers are far better because you can control how much you are feeding your fish every day so that little food goes to waste. Another option would be to ask a trusted friend to come by every couple days to check on your fish, feed them, and top out water levels if necessary.
Besides figuring out the feeding situation for your fish, you should also do a partial water change before leaving so that they have the highest possible water quality. And you should also figure out whether water levels are going to drop too much (through evaporation) while you're gone.