I see that now, as I read, thanks. The leaves reminded me so much of a crown of thorns house plant I used to have, but I know that house plant does not get berries.

Good detective work, kazoonative! Uconn is a great website. Autumn Olive is indeed classified as invasive in many states in the mid-west. People don't always see the effects of a plant's invasiveness around them. Some plants invade by runners, some by windblown seed - these types of invasion are more noticeable locally. Plants with berries (like this one) are usually spread by birds and the seeds can be dropped far from the immediate area. My neighbor has elaeagnus (not this one) and the birds deposit the berries in my yard - I pull out 5-6 seedlings a year. If I didn't, I'd have quite a few of these bushes already myself. Here is a link that might be useful: elaeagnus umbullata invasive information

It looks like Winterberry Holly, Ilex verticillata. That's not backed up by any evidence except that's what it looks like to me and I would expect it to be fairly common in NY state. They are largish, forest understory shrubs. WW Here is a link that might be useful: Winterberry holly

Can you get some closer pictures and tell us where this is growing geographically? Meanwhile look at Mahonia trifoliata and see what you think.