You can keep them going provided you can keep up the warmth, and the best light you can provide. The standard potting mix is okay, they do like the mix to be fairly organic. In the cooler time of year they don't need to be kept too wet.

tropic

Thank you. The soil was (still is) really wet. I have them under lights, but temps is only 58-60F. Wondering if that's enough?
(Droplets visible on Mojito are from me spraying - there were aphids on the new leaves...)

Rina

That converts to 14.4 - 15.6C which is very low. As a short duration minimum temperature that would probably be okay, but the bulk of the day would need to be a lot higher. I don't know what the cut off point for them is. You should aim to keep them above 20C.

tropic, Thank you, I will take them upstairs from the basement.
Or, perhaps store them? That could save me some space too. Found this on web:

In the winter, Alocasias and Colocasias should be dug right after the first light frost. After cleaning off the bulbs with water, I allow them to dry. The Missouri Botanical Garden recommends packing the bulbs in peat moss or wood shavings. They should be stored at temperatures between 40-50 degrees F. for the winter.

I have Amorphophallus konjac (number of corms now) that I usually just leave in pot without watering for the winter. They start growing 'whenever they decide' - just found one started sprouting recently. It is also in the basement, same temps I mentioned above (perhaps 'too warm' to overwinter?) and kept without lights. I didn't water it since it came inside, sometimes in early october.
I was thinking of doing similar with alocasia & colocasia.
Rina

Some people do let them dry out and go dormant, then they just store them for the cold season. When stored they don't want to be absolutely dry, they can shrivel away to nothing. But at the same time not wet either. To keep them growing they do need the warmth.

rina,
They aren't like your konjac. They can't survivie just keeping them
dry in shavings.
They need warmth and a little moisture, like a houseplant.
They will rot in too wet. That mushy is bad.
I would buy some fresh potting soil, and repot them in the dry potting soil and keep them warm, like advised above.
After you think they dried out a little, water them, not too much, they will rot.
I water mine that are in soil once a week.
I do have a tropical Colocasia in water, from my pond in the summer, I just took it from the pond since it was already in water anyway, and put it in a vase in front of a sunny window for the winter. I also feed it Foliage Pro, very weak, and it loves it.
Good luck with them.

butterfly4u

Thank you for additional info; I did get them out of that muck and cleaned/washed off the roots. I think I'll repot them into 'fresh' - new soil.

Do you keep the Colocasia bulb submerged in water or just the roots?

Rina