I want to make the largest character that I can without changing into another form. What spells, powers, items, or otherwise can I utilize in order to achieve this goal? Mention of size increases that can stack with other methods of increasing size would be most appreciated. Third-party material is allowed.
Multiple magical effects that increase size do not stack.
Meaning we now need to find a second, nonmagical effect to increase in size. In this case, we will look for abilities that are neither spells nor spell-like abilities.
Synthesist Summoner (8th or 13th)
A synthesist summons the essence of a powerful outsider to meld with his own being. The synthesist wears the eidolon like translucent, living armor. The eidolon mimics all of the synthesist’s movements, and the synthesist perceives through the eidolon’s senses and speaks through its voice, as the two are now one creature.
This allows you to summon your own personal translucent Gundam! (Remember, the Eidolon looks like the Summoner wants it to look like) Also, Fused Eidolon has no type (Sp, Ex, Su), so we can assume that it is non-magical (by RAW).
Take the Large Evolution and combine it with enlarge person to become huge.
An eidolon grows in size, becoming Large. [...] The summoner must be at least 8th level before selecting this evolution. [...]
If 6 additional evolution points are spent, the eidolon instead becomes Huge. [...] The summoner must be at least 13th level before selecting this option.
Or just become huge directly at 13th level, with the option for Gargantuan...
This works as long as your Eidolon is alive, which is as long as you are conscious, due to Life Link.
Gifted Blade or Psychic Warrior (7th)
You can also use the 1st level psionic power Expansion
This power causes instant growth, doubling your height, length, and width and multiplying your weight by 8. This increase changes your size category to the next larger one. [...]
If you spend 6 additional power points, this power increases your size by two size categories instead of one. [...]
You need to have a Manifester level of 7th to use 7 power points on one ability. Note that you can not combine this with any other method, since the power states:
Multiple effects that increase size do not stack, which means (among other things) that you can’t use a second manifestation of this power to further expand yourself.
The duration is the same as for enlarge person, 1min/lvl.
Expansion, the psionic counterpart to Enlarge Person, can be augmented to increase size by two categories instead of one. Starting with a Medium-size character, this will get you to Huge.
I know it's late, but for reference for others curious, the Advanced Races Compendium's Were-lion race can take feats at level 5 and 9 to make their Hybrid and full lion forms able to be large, then huge. They work as a Polymorph, so sadly no stacking RAW, though some DMs may override it. It seems that gives you +6 Str, -4Dex, +6 Nat Armor, and they typical huge changes. All-in-all, calculated out (late, so it may be off a bit) its a net gain of +1 attack, +2 AC (lost 2 DEX AC, and Huge costs 2 AC) but a total of 4 steps up on the damage chart of the FAQ. And of your DM let's you then take Snatch since there is no time limit on the forms and they are, flavorly speaking, a natural form, though Magical, you can slam an enemy and grab them in 1 attack, then throw them, and basicly be the classic movie giant monster as your allies can take advantage of your Huge distraction
If you play as the 3rd party awakened gargoyle, you can say that the person who made you set your size to large (technically any size, but I wouldn't push any further than large or the GM probably won't allow it) and become a psychic warrior which allows for you to grow to huge and later gargantuan.
If you want to be able to use colossal sized swords with your gargantuan sized character, look at the Titan Fighter archetype.
The Boots of the Winter Jarl from Reign of Winter Pathfinder Adventure Path Book 3 "enable their wearer to take the form of a frost giant", which does change your form, but it also makes you huge for 10 min per day without having to be any particular class or such.