Thanks all. Note that in addition to being a gardener, I love birds and in fact try to attract them to my yard via feeders, birdbaths etc. So I would never want to wantonly remove a haven for birds. However, I also understand the value of trees, which are unfortunately grossly under-appreciated, and their contributions grossly misunderstood, by most people in NYC. So this is why if I think a tree is at risk, that I should do what I can to save it. I also read a terrific book recently, "Bringing Nature Home: How Native Plants Sustain Wildlife in our Gardens", and it talked about this very thing...how non-native plants (such as English Ivy) can dessimate native plants/trees. As for those who mentioned that sometimes the ivy itself helps to anchor a tree, well I'd imagine that if a tree needs that kind of help in keeping upright, chances are it wasn't much longer for this world to begin with. But I'd suspect that in many instances, it's a case of ivy simply growing up and eventually masking an entirely healthy tree, and that eventually the ivy will block out its ability to take in sun. So at this point I still plan to cut as much of the ivy as I can without damaging the tree bark itself. Tx!

Some species of Passiflora.

Cissus incisa.

It could be a honeysuckle but I am leaning more towards Polygonum baldschuanicum. It would be helpful to see more of the plant and more mature leaves to be certain. As to whether it is poisonous, the honeysuckle is slightly but no more so that hundreds of other plants you probably have in your garden. More important that toxicity is the fact it will smother your Indian hawthorns if left to grow.