Delete the DiskCacheArena file under the swtor directory.
If that doesn't work, you can also try running a repair:
Non-Streaming launcher - Log into the launcher but don't click Play. Check for small letters "ST" in the bottom left corner. If this is NOT present, With the new launcher after login , select the username pull down on the top right and select settings, then press repair.
Streaming launcher - If the letters "ST" is present, close the launcher, right mouse click on the game shortcut, select open file location and delete the BitRaider folder. Then start the launcher.
If your stuck on another person's strong hold like a friend, have them kick you out so it puts that character on the fleet. If its the guild ship, they can remove you from the guild, once your able to log in, add back into the guild.
Worse case would be to submit an in-game ticket to have them get those characters unstuck. You would have to include:
Character Name
Server
Date / Time logged out
So they can move the character you cannot log into back to the fleet. Also note that after doing this you will need to also move to your ship or the fleet or somewhere other then a strong hold / guild ship till the bug is fixed.
For the characters that cannot go into your stronghold, you can try to deactivate that strong hold, then reactivate it again.
