It is possible for websites to disable the right-click context menu.

• http://kb.mozillazine.org/Prevent_websites_from_disabling_new_window_features

Start Firefox in Safe Mode to check if one of the extensions (Firefox/Tools > Add-ons > Extensions) or if hardware acceleration is causing the problem (switch to the DEFAULT theme: Firefox/Tools > Add-ons > Appearance).

• Do not click the Reset button on the Safe mode start window or otherwise make changes.

• https://support.mozilla.org/kb/Safe+Mode
• https://support.mozilla.org/kb/Troubleshooting+extensions+and+themes

Thank you for your response. Started in safe mode. Right click still does not work on aol.com. checked the appearance and it shows default 17.0 disbled. Checked other sites and right click works fine. Again, on aol.com, right click will work perfectly on safari or chrome.

Did you try to disable plugins as well?

• https://support.mozilla.org/kb/Troubleshooting+plugins

You can create a new profile as a test to check if your current profile is causing the problems.

See "Creating a profile":

• https://support.mozilla.org/kb/profile-manager-create-and-remove-firefox-profiles
• http://kb.mozillazine.org/Standard_diagnostic_-_Firefox#Profile_issues

If the new profile works then you can transfer some files from the old profile to that new profile, but be careful not to copy corrupted files.

• http://kb.mozillazine.org/Transferring_data_to_a_new_profile_-_Firefox

I tried it in safe mode which I thought disabled everything.

Safe mode only disables extension and doesn't affect plugins.
If you want to test for plugins then you need to disable them yourself in Tools > Add-ons > Plugins.