I never said it wasnt a good troubleshooting step; however, launch agents are very unlikely to "become corrupt" since they are more often than not files that are just read by the system launcher (launchd). Even though they are "plist" files, they are not like preferences files which are regularly read and written to, and which therefore are more prone to corruption.
You are incorrect that launch agents are files that programs recreate each time they are run. In some cases yes, but in most cases launch agents are NOT recreated. You might be mistaking them for preference files, but launch agents are largely placed in these locations by an installation script and are then not maintained by respective programs.
Additionally, if a launch agent is corrupted then at most the targeted task will not load properly and you will get regular errors in the system logs by the "launchd" process. Even rapid logging by this process has neglegable impact on system performance, and will not affect how other programs (i.e., Firefox, Opera, Safari) run.
The exception is perhaps a malicious launch agent installed by malware, which may try to launch additional malicious code, but this is a rare occurrence. Nevertheless, it is a possibility, and my recommendation here is to list the launch agent scripts by name in a forum posting here so people can help determine which may be suspicious.
It is also incorrect to presume removing all laungh agents blindly is "completely safe." If a third-party program you use requires background tasks to run that are governed by the launch agent, then removing it will break this functionality and leave you with more frustrations than you started with.
Because of this, blindly deleting launch agent scripts is simply not the best approach. If any troubleshooting regarding them is needed, then remove them from their parent folder and then log out/in or restart to load them properly, but keep them around so they can be manually restored.
If the problematic behavior continues after removing them and restarting, then they should all be restored. If not and the problem seems fixed by removing them, then you can restore them one at a time, rebooting and testing between each in order to see which might be contributing to the problem. If the system shows the problematic behavior after adding a specific launch agent back and rebooting, then you can open the agent file to see what tasks it is launching, and further investigate the issue.
Again, the preferred approach here is to list the names of the launch agents here in this discussion forum, and have folks provide input on which ones appear valid and which ones (if any) appear suspect, and then further investigate them.
Regarding the original poster's problem specifically, one first approach would be to check the Users > username > Library > Internet Plug-Ins folder and similarly troubleshoot the contents of it by removing them, seeing if problematic browsers start working, and then adding them back one-by-one if so, or adding them all back if the problem persists (since it would be clear the plugins were not the cause of the issue at hand).
Before doing this, however, its recommended to try creating a new user account in the Users & Groups system preferences and logging into it to test the browsers in there. This will help determine if the problem is with the user account configuration, or more global in nature.
I recommend the original poster try these approaches first, and report the results back here.