I am using TortoiseHG version 2.4.2 and with either firefox or internet explorer I can browse the following codeplex project just fine.
https://hg.codeplex.com/oxyplot>
Amazingly enough, Visual Studio 2010 Professional was the answer I was looking for. Or rather, VS2010 + HgSccPackage extension. For those who don't know HgScc is an extension for VS that gives it native Mercurial support.
Something that kept bugging me was that I could browse the mercurial repository using my web browser, but NOT clone it with TortoiseHG. After I posted my earlier update to the question, on a whim I just tried browsing the repo from VS2010. Surprisingly enough, I was able to! Well, then why not try and clone the repo straight from the IDE then? So I did, and wonder of wonders, it worked! :)
No bothersome proxy settings or any of that nonsense. After the extension is installed, from the menu bar select,
Mercurial > Clone
In the options there I just pasted the source path to the project as depicted by Codeplex, filled in my Codeplex authorization info and finally the destination where I wanted the project copied to.
It worked!
In hindsight, I'm certain that the reason why this worked is because the hgscc extension uses the default VS2010 (or rather Internet Explorer) connection options and not it's own as tortoiseHg does. Which implies that the VisualHG extension would fail as it's just a wrapper around tortoiseHg to begin with. I haven't tested this, but if anyone does, could you leave a comment?