I am travelling to the USA (Texas) and would like to bring some of my home-dried vegetables for myself and for my hosts. I have read and heard conflicting information about this issue, so I would like to be sure: is this allowed, and if so, how can I do this? Should I put the vegetables in vacuum-sealed bags?
Absolutely say you have something to declare. If you declare it and show it to the customs officials it won't take any time at all even if they confiscate it. They will just take it and you'll be on your way. If you don't declare it and customs finds anything they'll look through all your luggage very thoroughly and enter your information in the computer, which takes quite a while. They might also fine you.
It's complicated but the answer appears to be that this is probably allowed.
You will have to declare your vegetables at customs when you first enter the US (in your case that will be in New York). Agriculture inspectors will then look at them and decide whether you can keep them or not.
Here is the guide used by the inspectors. Dried fruits and vegetables are covered in Table 3-130 on page 3-98. It seems like only a few specific types of vegetables are forbidden.
Note that this guide seems to be written mainly to deal with commercially dried fruits and vegetables. I didn't find anything that specifically addresses home-dried products.
These regulations are handled by the USDA APHIS service. If you want a more detailed answer, you could contact them and ask.
My personal experience says, unfortunately you can't be sure about it. :) however... there is a higher probability you could pass all your food without any problem, and a lower probability for being questioned for a (re-)inspection by a suspicious officer which could lead to throwing your dried vegetables (and of course other foods which seem unfamiliar to him/her).
Maybe you could take some commercial ones with you as alternative in case such thing happens. In general try to substitute home-made ones with commercial ones as much as possible (I know they have lower quality but at least seem less suspicious).