In the UK, we would say the following:
The vegetables are stale ("stale" can be used, but it's not so common for vegetables)
The vegetables are out of date (i.e. out of the recommended dates of consumption)
The vegetables have gone off (e.g. past expiry date)
The tomatoes are bad
If they look really bad (e.g. tomatoes), you can say:
The tomatoes are rotten.
Hope this helps!