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The problem you should worry about is the interaction between your group and your GM. "Breaking" your character's damage output won't matter. The GM is completely in control of the game and nothing you can do to your character will change that. You should talk to him/her about your concerns about how they run the game. If they're not willing to change, it may be time to find a new GM.
Pandora's is correct. You can never win an arms race with the GM.
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It seems you have made some errors. First, Furious weapons don't allow you to rage, you need to be able to rage via barbarian/bloodrager/skald class feature, or be able to rage via casting the rage spell. So you should cast it to get the +5 weapon you want.
You can't wield a large-size two-handed weapon as a medium character unless you have an ability to use such, or your GM allows it, so you really should be doing less damage with that greataxe. As to mythic vital strike, you should be doing 9d8 when you vital strike even as mythic, because the bonus dice from your vital strike isn't multiplied on a crit. You should be getting 3*[1.5STR+PA+enhance] on it though.
The Gug had some serious HP, but might have been able to do it barely if they had templates and mythic stuff added. 5 of them is too much, but if it were a solo encounter it may have worked.
But anyway, there is little you can do if your GM cheats unless you talk to him about it. Pumping your damage will always come at a cost, and it will always be exploited. Talk to your GM and see if you can convince him to go a bit easier. Otherwise it just develops into an arms race between player and character, and you will go from a campaign to a hack-slash game. Its happened to me, and instead of ruining the friendship with the GM, one of the guys I game with regularly offered to run something different sometimes so that the GM could play a bit, and he decided to go easier.
As a GM, I often casually throw extra HP onto enemies if I feel the encounter will not be challenging, or in more extreme situations use the advanced template or extra class levels. If I do not intend a fight to be challenging, I will rarely play it as actual combat, and more as a roleplay situation. If I do intend a combat to be challenging, I will make sure it is, no matter how much you maximize your build. As Pandora's said, please do not try and arms-race your GM.
Pandora's is correct. You can never win an arms race with the GM.
If the GM like to play for the rules and maintain a "realistic" progress for the adventure i think you can win.
I've already tried to talk to the DM, he's not going to change his ways. He's the only DM we have. Returning to the original reason I posted, what feats/classes/etc can I take to increase my damage/survivability?
If he works any bit like I do, you don't need to take any. The stronger you get, the stronger he makes the encounters. Make the most enjoyable character possible, not the strongest, because you won't actually make combat easier on yourself.
Yeah you can't beat a GM. Sounds like he might be burned out and is hoping someone will take the GM seat. You could have a uber character and he will just make a uber+ opponent this is definitely a real world issue and not a character one.
What is the rest of the party? Can they help with damage through teamwork, like flanking, buffing, aid another, etc. etc.?
yo, the furious enchant doesn't grant you the ability to rage. it just gets more powerful when you rage (from the class feature, rage domain thing, or the spell)
About this:
"Mythic vital strike lets me times all my damage modifiers that would get the critical modifier on a crit by the number of dice the weapon does when I vital strike (without needing to actually crit). Now this should be x9 because I do 9d8 when I vital strike, but the DM ruled it uses the weapon's base damage dice, although if I was using a normal sized single die weapon like a longsword this would make the feat give a x1 damage multiplier so it would do nothing and make the feat USELESS"
In actuality
Mythic Vital Strike
You can strike your foes with incredible force.
Prerequisite: Vital Strike.
Benefit: Whenever you use Vital Strike, Improved Vital Strike, or Greater Vital Strike, multiply the Strength bonus, magic bonus, and other bonuses that would normally be multiplied on a critical hit by the number of weapon damage dice you roll for that feat.
Extra damage from sources that wouldn't normally be multiplied on a critical hit isn't multiplied by this feat.
I believe you are misinterpreting the feat. The feat doesn't let you add that for each die rolled it lets you add it for each set of weapon dice rolled.
Vital strike lets you add your weapons damage dice in one extra time but without the bonuses. IOW, 1d8 for a long sword or 2d6 with a 2handed sword but without the bonuses.
Mythic vital strike when coupled with vital strike lets you add all those bonuses in 1x because you added one set of weapon dice.
Improved vital strike would let you add 2d8 for a long sword (without bonuses) or 4d6 for a 2 handed sword without bonuses for either.
Mythic vital strike when coupled with improved vital strike lets you add 2d8 for a long sword or 4d6 for a 2 handed sword with double the bonuses.
The point here is that the party is a group of mythic characters and the DM is creating encounters that are challenging. I don't see any mention of such and such player has gone through eight characters and someone else has gone through five.
The party should be facing multiple creatures with a CR above their party level. Why? Because A CR 10 being a threatening encounter for 10th level characters is assuming four characters and does not take into account that the party is made of mythic characters.
So, I don't actually see the problem here.
Why is it a bad thing that a group of mythic characters are repeatedly facing difficult encounters they are surviving?
I do kinda find it funny when you have characters with extreme damage builds, which might technically be legal but occur through bending of rules (of intent, at least), then wonder why the GM turns around and warps the setting too.
Tho for mythic stuff, when you're not facing mythic stuff, you're going to tend to paste anyway. I'm partial to Blowback myself, "Hah, I hit you and you go flying 50 feet, no save. I don't care how big you are!" Raw damage is ok. I lean towards amusing epic hit visuals :)
If it were me, I would just say "I'm not having fun with this. Let me know when there's another opportunity to play in a game that doesn't feel so combative."
There's better things to do with your time than play with a Typhoid Mary GM.
If you really want to maximize your damage output pick up the Legendary Item mythic power and give your sword the power that lets you resolve attacks as Touch Attacks. That's about all you have left to add to that build.
As have been noted, you shouldn't be able to use an oversized two handed weapon. The sole exceptions are the Bastard Sword and Waraxe, which require exotic weapon proficiencies. The Transformative weapon property also helps negate the problems with wielding oversized weapons if the base weapon is large enough.
With your build you should be dealing plenty of damage. It barely matters what weapon you use. The majority of your damage output should be coming from static bonuses.
HP is something the DM can easily adjust. Maybe on the fly, maybe for the next combats. You won't gain anything by optimizing your damage continuously, unless your DM is fine with encounters just rolling over. And they might be, I know I'm okay with that. It's up to you to decide if that's fun.
Does this DM roll behind a screen? If so then tell him to stop hiding his dice like he's ashamed of them and start rolling them in the middle of the table for all to see and fear.
After that I'd suggest optimizing not damage output but your defenses. Even a PC who does mediocre damage can win fights if he or she can stay in those fights round after round. Defensive builds tend to drive DMs fairly nuts too, but unlike DPR machines they don't end fights prematurely and deny the other PCs a chance to contribute. DMs can get pretty frustrated when they feel like they can't hit your AC, but it seems less likely to cause a major arms race.
Anyhow, what mythic path is your PC on?