There are a few classes you can multiclass into to gain skills, such as Bard, Ranger or Rogue.

In addition to that, in the player's handbook there is a feat called "Skilled" which allows you to gain proficiency in any combination of 3 skills or tools.

In Xanathar's Guide to Everything, we have the Prodigy feat which gives a skill proficiency and a few other things, but can only be taken by a Human, Half-Orc, or Half-Elf.

In Tasha's Cauldron of Everything, the feat Skill Expert gives proficiency in a skill and a few other benefits, with no racial prerequisite.

There is also a bard ability in the college of lore that allows you to learn 3 more skills at level 3.

Currently, the downtime rules allow you to gain proficiency in tools but not skills.

In case it isn't clear, you don't have to pick skills from your class skill list when you gain new skills through the "Skilled" feat. You can pick any skill you want.

Alright, it sounds like you have a lot of problems going on here that I'm going to address individually using the ruleset that you've chosen for your game.

First off, you're being taken advantage of.

There's no easy way to say this, but your friend is attempting to take advantage of you during the course of this game that you're playing. An item to double someone's Strength score (whether it be armor or a belt) would cost millions of gold pieces and be at least an artifact level item. Under zero circumstances should you ever agree to such a demand within the confines of the rules. He can buy a +6 Belt of Giant Strength just like everyone else.

A barbarian (no matter how "special") can't determine whether an item is magical unless you the DM make it obvious.

A magical item has a 20%ish chance of having a magical glow that would indicate that it's magical. It sounds like in this instance your item has this, so a check isn't even necessary. If you want to know its magical properties (and you do not in fact have access to the Wizard spell Identify), your barbarian must roll Spellcraft with a DC of 70 + caster level of the item. If he can't make that check? Tough. He can't identify the properties of the item.

If you want to be nice you can use the following descriptors in my answer on this question to give the players a hint at the items purpose. But that's entirely optional.

Sunder doesn't work that way.

With sunder there are steps that you need to follow, that are written so a Barbarian doesn't steal your sword and attempt to snap it over his knee.

You take an attack of opportunity, and you roll an opposed attack roll. If he wins? Deal damage to the sword or shield or armor as per the hardness table for materials in the DMG. If he has Improved Sunder he doesn't incur the AOO. There shouldn't ever be an occurrence where process fails to happen if he's attempting to break a weapon. If you cave on this guy you're showing him that he can bully you, the GM, around, which complicates things.

What he's attempting to do with a door isn't really sunder, and ties into the type of door he's trying to use brute force to break through, and the Break DC of that door. Wooden doors are the easiest to break through, then stone, then iron. All the information about doors, and their break DCs can be found here.

"The rules don't say I can't" isn't a valid argument.

The rules don't say you can't, but the rules don't say a lot of things that common sense would normally take care of. The rules don't say a wizard can't spit lasers or vomit lightning at will, but the rules do say what you can do within the scope of the game. If the rules don't say you can't, it also means they don't say you can also. What information isn't covered by the book can just be fielded by common sense, or house rules.

He's attempting to punch through a door?

Bones aren't as strong as iron or stone, or even wood. If he attempts to punch through an obstacle that isn't meant to be broken he breaks his fist, suffering a penalty to all melee attacks until he receives healing of any kind. Making other players useless is awful. It's even more awful if its allowed to happen. So make him useless for attempting to act outside the confines of his role. This will teach him some humility hopefully.

The best way to get rid of this mentality is to punish his kick-in-the-door style of play. There was a module a long time ago published called The Tomb of Horrors in which everything was a trap meant to screw with and punish characters or players with preconceived notions on how the game itself was played. It had things such as Pit traps with poisoned spikes (Save or Die), fake doors that when opened or forced will conjure a spear to stab the closest person, a sphere of annihilation for those who attempt to backtrack to an area after they fell into an area triggered by a prior trap, and secret doors hidden slightly above spikes at the bottom of pit traps.

If you do play something like this module your barbarian friend will trigger every trap, die, and then he can roll up another character, but if you do decide to run something similar to The Tomb of Horrors be sure that everyone you're playing with has at least a minimum of two characters on hand, there will be lots of death involved.

Puzzle doors.

If your barbarian friend is that insistent on trying to brute-force his way through solid objects, implement a series of puzzle doors that require brainpower to solve instead of trying to punch things. It will give your group a chance to converse at length and find a way through the doors using thought and teamwork instead of one guy attempting to brute force through something he has no business trying to break.

Create a skill challenge that requires the Barbarian to be preoccupied while the rest of the party solves the rest.

Lets say for example your party is in a dungeon, and there's a portcullis in a dungeon. For those of you who don't know a Portcullis is a door normally with bars that falls down instead of opening up. They normally have bars. For this example we'll be using a standard portcullis. On one side of the gate is a large iron wheel which connects to a chain that when turned will raise the Portcullis, However, the wheel is rusted and requires great strength to turn. Once the barbarian turns the wheel, as its pretty much expected for him to do, he will have to attend to the wheel to insure that the Portcullis remains open while the other PCs finish their own challenge.

"Now today he is demanding that I allow him to seek out something called Thor's Belt and win it from him in a contest."

This is probably your best opportunity to shake the mentality that because he is a player and your friend he gets whatever he wants. Put your foot down. Let him fight the level 40 Demigod with over 1200 hit points who always hits and only has to roll to confirm criticals, with DR 71/+5 and ninety-two strength, to get his belt.

The fight will end in one round and he can roll up another character that might be a little more humble. If you don't want to be this drastic you can do this outside the actual canon of the game to show to him what a ridiculous notion he's attempting to pass.

If you want to be less drastic...

Just give him a warning. Just warn him that what he's attempting to do doesn't exist or function within the confines of the game rules and if he raises an objection put him in time out for five minutes while you resolve combat for the people who DO want to follow the rules. If he doesn't want to follow the rules, time him out for five minutes. Eventually he'll get the picture that what he's doing isn't all right, but you're going to have to be strict.

What he's doing to you isn't okay. His actions are railroading the game the way HE wants it to be played, not the way you're trying to run it, and that just isn't a cool thing to do at the game table.

"And as of today refuses to cite official source books stating the wiki is always right (not the dndwiki.) Therafim. And not in any srd section."

While there are valuable tools online for 3.5 related games, such as the Online d20 SRD, Herolabs, etc., sites such as Dandwiki, D&D Tools, and Therafim should be taken as sources with an extreme grain of salt. Oftentimes things on Dandwiki are homebrew content unless specifically marked with the "SRD" descriptor on their title pages. And generally Therafim and D&D Tools (while usually having correct information) host their information illegally: most information you find published on those sites is from books not covered by the OGL.

If he doesn't cite the sources for his character decisions from actual sourcebooks, I would make him find the information before allowing him to even sit down and play at the table, as there's a possibility that he could even be making it up as he goes along to give himself an edge. If he can't find the information about his abilities in an actual sourcebook, have him roll up a new character with the books you have at the table.