Love that idea, Rick! I'm not good with orchids, but if you have a window that they would like, you can hang bunches of plants by putting a closet rod across the top of the window (from wall to wall if possible)... and if you can't attach a rod to the wall (call it a "window treatment" and the landlord may allow it), maybe you could make a frame to support the rod (upside down T's with a notch or hole at the top of the upright post).
I saw the title of this thread and actually thought at first it was a suggestion to use this strawberry planter for orchids... Not sure how to make that work, but you could definitely use a length of PVC to make a "tower" of hanging orchids (a little hole and an s-hook, and you'd have a hanging place)... either make a base to support it or just wedge it between the floor & ceiling of your patio.
In fact, if you're not especially "handy," it might be easier to put together a PVC frame like RickM suggested than to nail 2x4's together. There are straight connectors and elbow connectors for PVC pipe... it's like an adult version of tinker toys.
I don't know your zone, or your condo regulations, but maybe there's a way to enclose your patio with removable plexiglass panels in order to create a little greenhouse for your orchids.
Best to you!
