Crazy roots!
 

I inherited these (pic attached).

How do I re-pot them, i.e., what do I do with the huge roots?

where do you live and what is your growing area like? it has a lot to do with how you make these new ones happy

First, soak the roots for an hour or so, to make them more pliable. But don't even THINK of getting them all into a pot. Take the plants out of the pot, clean off whatever medium comes off easily. I suspect that it is very broken down, so roots within the pot may not be any good (which would inspire the wild outside-the-pot root growth. Clean off any rotted velamin (the coating on the roots in the pot) but if the roots are still firmly attached, leave the stringy middle of the root, it can help hydrate the plant but even more important, help to anchor it firmly in place in new medium. You can go to a somewhat larger pot (but don't over-do it, pick one about the diameter of the leaves) You can gently coax some of the wild roots into the new pot, twisting the plant to try to wind those roots around. You may crack the velamin on some, the root is still viable, but better of course not to do that. If the roots have softened up enough from the soaking, hopefully they're pliable. Then what doesn't go easily into the pot, leave outside. With a more "friendly" environment in the pot from new medium, new roots will grow into it. Remember, too, that the new medium will dry out much faster than the old, so you'll need to water more often. If you choose something airy, like medium bark, you can't over-water... the roots want "humid air" instead of "wet". Air is the biggie.

Thank you.

Once new roots develop in the new potting media will the ones outside of the pot eventually wither? Would I trim them or after they develop new roots?

Don't cut healthy roots. Period. The ones outside the pot may keep on being healthy for multiple years, especially if they continue to get moisture (like misting) . And they're contributing to the plant. If you need to get them under control, a trick I have used is to drop the plant (pot and all) into a substantially larger pot (again gently twisting the plant as I guide the roots into the larger pot so that they wrap around). Don't use any medium between the outer big pot and the smaller one that contains the plant and medium. That air space between the two pots can give a "humidity boost" to the air roots, they are in open air so you don't have to worry about soggy-medium rot which you could get if you used a too-large pot with medium. The air roots are happy because they are getting a bit of humidity with air, you are happy because the roots aren't taking over the house. :lol:

dont cut roots. even if they look dead. if they are actively wet and mushy, maybe, but i still just remove the rotted parts and leave as much as i can.