Well, I think most people have probably endured what you're going through right now at some point or another.
There are several ways you can handle it from my experiences. One, would be just to take a break. Stop roleplaying for a while. Perhaps even tell your partners that you're taking a vacation for a week or two and you won't have access to wifi. When you are having down time, read a book, watch a movie, do something besides roleplaying. This is a really great option if you don't actually hate the partners/plots/characters, but are just burnt out on roleplaying. Sometimes, it happens. Sometimes, you force yourself to write so much you just get disgusted with it. Taking a step back for a while will help.
Second, is to try and work through it. For me, this is usually what I have to do. I don't take breaks from writing very often. Even when I feel like my writing is the worst, and I'm having a terrible day ripping myself apart for my "bad" writing or hating my characters/plots/partners, I keep writing. I find it's easier to get out of a funk when I just keep writing through it then if I try and take a break. It's incredibly difficult for me to get back into it after I take a break, mostly because I get lazy and don't want to do anything.
I work 60-70 hours a week, but I will take my 15 minute breaks or my lunch and bring my computer outside (on nice days) and just try and throw out 1,000 words, even if I'm not really feeling it. Other times, when I have a day off, I'll take myself to a café, treat myself to a nice coffee, and will force myself to write. I find it's a lot easier to write when I'm in public than in private (I guess because I can't get distracted with video games or food? :P )
For me, it all comes down to routine. If I sit down at write 500 words every morning before I go to work while I'm having my morning coffee, it's so much easier than trying to just write when "I feel like it." That being said, even when I'm not roleplaying, I like to chat with my partners. The people I've had the most luck roleplaying with are the people I've become friends with. When I don't feel particularly like posting, I'll shoot my partner a friendly message and begin plotting about future events in the roleplay. Nothing gets me hyped up more than going back and forth with my partner about future events. Suddenly, I'm excited for my roleplay again.
As for hating my characters, I usually end up thinking about what in particular I don't like about them. Are they boring? Are they a mary sue? Are they... I dunno... too ditzy? Usually, I pinpoint out a few things I find terrible about my character and figure out a way to change them. For example, in a roleplay I had not that long ago, I found my character to be boring to write because he was kind of blase and a stick in the mud about everything soooo... I found a plot loop that forced him to change. People change all the time based on events in their life-- so why can't characters? If you don't like them how they are, give them a reason to change! Going back to my character, I ended up blowing down his house with a tornado. XD He became considerably less boring once homeless.
