This fix may be a bit tricky for some depending on who you know but if you have a friend with a PC version of skyrim you can fix this glitch and continue playing your game.
In my particular save I was on the Jagged Crown quest when I received Season Unending and encountered the error where I could not properly converse with Ulfric to progress the main quest line. This is what I did to successfully get past it:
1) Plug in a USB stick during gameplay on your 360 and make a save on it. 2) Open that save with Modio, this is free software that you can use to modify your 360 saves. 3) Click File Contents, right click savegame.dat and extract. 4) After extracting, rename it to savegame.ess
At this point you need access to a PC version of Skyrim. 5) Move the savegame.ess file into the Skyrim gamesave folder on the PC and then load it up 6) After it loads, hit the tilde key "~", this will bring up the console command UI. 7) At this point type in "setstage CW02B 200" 8) In my particular case, this advanced the Jagged Crown quest, and I was able to then talk to Ulfic and continue the main quest. 9) Save game, exit, then rename save back to savegame.dat 10) Go back to modio, open your save on USB>File Contents>Right click savegame.dat>Replace>Select the new save. 11) Click "Rehash/Resign" 12) Click Save to Device
When you load your save back into the 360 you should be all set.
Now for a few notes, with the setstage console command, CW02B is the code for the Jagged Crown quest and 200 was the particular number to complete it. If your glitch occurred on a different quest you're not out of luck, just search for the particular quest on uesp.net and you can find the quest ID and the stage you have to set it to for completion. Good luck to everyone that encountered this error and I hope this helps some :-)
If you're on jagged crown and then receive the Unending Seasons quest it won't work. When you go to talk to Ulfric he says to talk to Galrund or whoever the guy is but when you talk to Galrund he has dialogue for the seasons unending quest, this becomes and infinite loop which you cannot get past. I even went to Korvajund to attempt the quest but that won't work without Galrund coming along which he wont. You must have been at a different part in the quest since you got past it.