For outdoor plants, definitely spring and fall are the best times (although I'd never say "never" for planting at other times). For indoor plants, you repot them when they need it. Yours most definitely needs it, the sooner the better if you have any hope of saving it.
As already suggested, it needs a pot with a drainage hole, lighter soil, and I'd also trim back the stems to almost halfway to see if that helps force any new growth. Those stems do look pretty dead from the photo though, but it won't hurt to try if it has some sentimental value.
