First off, you get two points for using the word, "incredulity." Secondly, you get extra points for the use of your cartoons, as they were spot on.
This crap REALLY gets to me. Some people are just SO stuck on their opinions that they are unable AND unwilling (as opposed to being EITHER of them) to accept the possibility that ANY facts contradict their opinions.
To these people, after you have given them the good fight and TRIED to use logic and fact (like a biography of Tolkien!!), you must - for the sake of sanity - just loudly label them as being RONG (that's when a person is SO wrong that they can't even spell it correctly) and ignore their very existence. To do anything else is pure folly on your part. It's like that old analogy of wrestling with a pig in mud - you will never win, and they LIKE it!!
I have used a flame-out approach. Set up a word-processing document and craft your final reply to them - pointing out each and every detail that demonstrates their idiocy, and using GOOD internet linkies to provide them with good references (NO Wikipedia!!), and even include short quotes using hyper-tags to support your points. use the most mature tone you can (don't resort to flame-baiting or name calling!!), and then post your response. If the gods smile upon you, the person will be shamed into silence or will never again visit the board... and your response will garner the respect of other people that are willing to look at opposing viewpoints and opposing opinions dispassionately.
If that doesn't work, get their e-mail address and sign them up for interwebs porn mailing lists.
I feel your pain - been there, had to learn the hard way to survive that. Good luck. (some idot (too stupid to spell "idiot" correctly) thinks Tolkien stole WARCRAFT orcs?? OMFGWTFBBQ!!!)
EDITED TO ADD:
I'm sorry, but the Tolkien/Warcraft thing got me so bothered that I ignored half of your question...
For in-your-face situations, the ONLY thing to do is to either seek support from the rest of the group in shutting the idot up - OR leave the group setting, which can be impossible if it's the only game in town. Outside of this, just look at them straight in the eye and tell them that this topic is something that you will NEVER see eye to eye on - and for the sake of gaming, it is time for BOTH of you to bury the hatchet and never speak of it again. If they are mature, they will agree. If they aren't, then you MUST resort to either getting the rest of the group involved or leave the game.
Be mindful of little jabs from this person afterward - like mentioning Tolkien or Warcraft stuff during the game. Most folks that do this are also passive aggressive, and will try to get a rise out of you until they get their way. If this happens, look at them so they KNOW you heard it, and the second time you hear it, ask them why they aren't mature enough to bury that hatchet. This will almost always get them so upset that they will lose their cool - and it's a LOT easier to get them kicked out of the group after that.
I saw a guy vault a gaming table and start beating on another guy for suggesting that green dragons were puny and easy to kill. The big problem for him was that the suggester was into judo, and subdued him - then we ALL threw him out of the gaming store.