Okay , here's another good shot of me. :) Enjoy!
-happy little dend.
That looks like floral foam in the pot. I have seen it used as a single little piece (plug) to start baby plants, but that is the first time I have seen it for a whole big plant. As you say, a lot of these things are meant to be tossed after flowering, and this is obviously one of them. I have no idea how to care for it in that chunk of foam (soak the foam when completely dry, but make sure to let it get completely dry between waterings, would be my guess).
I would say you have two options: 1) let it keep growing like it is and hope that it over grows the pot and roots go down in between the two pots befor the roots in the foam die. You can grow it like a mounted orchid that way. 2)what most people would do is wait until the flowers drop and a new cane gets about 2-3 inches high and at that time pick all of the foam off of the roots and repot into a bark or coconut husk chip potting mix. Use the same size pot, probably go with the clay. The new cane has to be that big because that is when new roots will be produced en mass. Repotting at any other time will cause the plant to sulk for a long time. These plants also like to be rootbound in small pots. They are usually repotted only when they are really over growing the pot.
That looks like one of the larger mini Dens (compact Den.) It probably has Dendrobium bigibbum var compactum or Den. superbum as a parent. Both are closely related to Dendrobium phaleanopsis.
I would leave the plant in the Oasis. the plant will be fine provided it doesnt sit it water. are there drainage holes in the base of the pot? it will need fertilised using an Orchid feriliser once a month. you should be able to buy 2 sorts. one for while in bloom and the other while growing. dont push the new roots into the foam but let them hang free.
Dendrobiums need to be stimulated in order to repeat bloom. I'll check one of my books and get back to you with optimum growth temperatures.
Thanks everyone. It's in a plastic pot inside that clay one you see. It's that okay? I'm a little hesitant to keep it in the plastic one. Should it stay?
Taking more opinions. I've got one "leave it there" one "get it out after flowering". :)
-THLD and Jennifer