As Mike said, it sounds like there's a plugin / addon that is hijacking all of your traffic. Pretty common, and fortunately very easy to fix.
First, check through your installed programs and look for any toolbars / adware junk. These commonly are installed with freemium / shareware programs, and can easily be remove. The uninstaller often doesn't remove the browser changes, so you'll have to do those manually as detailed below.
In Firefox/Pale Moon, go to about:addons and disable either everything, or those that you are not familiar with. On the left you should also see Plugins, and some of these you may wish to disable as well.
You can launch a browser in its safe-mode, which should disable all of these addons/plugins. Here's a link to do this in Firefox
(I would assume Pale Moon is the same).
Chrome does quite well with their reset browser settings dialog, found in the advanced options of the program. Here's a guide to find it
if you don't have any luck.
Internet Explorer should have similar options, but I won't bother detailing them since it's unlikely you'll end up using IE.
If none of these fix the problems, you may have some DNS entries that don't belong. It's not super common for this to happen, but if your DNS entries are set to a malicious third party, they could be giving you junk pages instead of what you'd want. Change these back to "obtain automatically", or to your own DNS preferences.
After ALL of that is done, don't forget to change your homepage back to whatever you'd prefer. Adware tends to change search settings as well, so while you think you might be using Google or Bing, you're actually using SuperSpeedyJunkySearch.com or whatever. That's the benefit to resetting the browser settings, as this should be wiped out.