I have attached orchids to trees before using Liquid Nails. It comes in tubes like caulk and is used for putting down tile (I think). It works great and doesn't adversely affect the plant at all. Just don't get the glue on the roots. I glued some catts on the trunks of Queen Palms and they look nice.
I used the natural bumps on the trunk to rest the rhizome or old pseudobulb on. I move it around until I find a position where the roots fan out in a natural direction. Then, I put a glob of the glue on the trunk where I have determined it will sit naturally. Place the plant on the glue and cover it with a little moss. Then I wrap it with that green plastic ribbon they sell at home depot in the orchid section. I like it better than fishing line because it doesn't cut in.
I leave that on for a couple weeks or until it has gotten enough root tips growing to look stable. The tape is actually just to hold the moss in place. You can take it away as soon as it doesn't need the moss any more.
Here are some pics of one in my front yard. I always put them on the north side of the tree for extra shade. In the corner of the last pic you can see a little bit of the glue still. The rest of the glue has been covered by roots or bulbs. This was probably attached about 1.5-2 years ago. It was a half dead orphan so I figured what the heck? One last chance and it really took off. I have no idea what the flowers look like. Hopefully it will bloom this winter!