Recently I've had this idea for a kind of combat wizard, maybe a half orc that starts with a high intelligence and a decent strength, uses a greataxe(since they're proficient), and uses mostly polymorph spells to be good in combat. Transmutation school would allow a increasing bonus to strength as I level, and polymorph spells would allow me to be decent in melee combat.
Do you guys think a character like this would be viable and/or fun to play?
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What your after would be known as a "gish" and it has existed long before Pathfinder. The "melee wizard" is a tried and true concept and, in 3.5e D&d was very viable with prestige classes like Abjurant Champion. In Pathfinder, being a "gish" is a bit trickier then it was in 3.5e due to the fact 3.5e had a lot more prestige class options that made you good at being a fighter/wizard. However, don't let that dissuade you, as Gishing can still be done in PF -if- you know what your doing. Sadly, I am not all that knowledgeable with PF gishing since I am somewhat new to Pathfinder and usually play straight casters as appose to gishes. However, I do know some very basic stuff I'll throw your way..
Straight wizard is a poor idea for a Gish. Yeah, polymorph spells are a thing, but you can't always cast them and thus you WILL have to, at some point, rely on your own base attack bonus. Since wizards get crappy base attack bonuses, it's almost always better for a gish character to multiclass into something like fighter and then take a prestige class that boosts both your melee fighting skill and spellcasting. In pathfinder, I only really know two such classes, and only one of them can be taken by a wizard. The class that is "wizard friendly" would be the Eldritch Knight. Eldritch knight boosts your casting at every level except 1st, and gives you good BAB as you progress through it. It also gives you a small number of bonus feats that are focused around combat. As an eldritch knight your BAB won't be as good as a pure melee character, but it will be -passable- for a melee character and far better then a straight wizard. Your spellcasting will be a big behind due to the CL hit at level 1, so you should invest in a CL raising trait like Magical Knack to help that.
If you are not 100% set on being a wizard, however, Dragon Disciple is an awesome class for gishes. Dragon Disciple means you have to be a sorcerer or bard(I'll assume sorc since your interested in a wizard?), but unlike the eldritch disciple which gives you basically nothing other then high BAB, casting progression and a few bonus feats. Dragon Disciple, however, gives you all kinds of cool class features that are geared largely towards being a magical melee combatant. The only downside with Dragon Disciple for you would be A) you can't be a wizardly dragon disciple as far as I know/you gotta go sorc or bard to enter and B)You use natural weapons for melee combat a lot as a dragon disciple which may not fit with your "axe-swining half-orc" image.
Again, if your ok with playing a class other then wizard the Magus does exactly what you want without having to plan out a complex build. It does melee well and is an int-based, arcane caster with a strong spell list. Heck, a Magus even gets a spellbook like a wizard! The only thing with a magus, though, is that while they are a "gish in a can" their spellcasting is weaker then that of a wizard. They only get up to 6th level spells and their spell list, while good, is weaker overall then the wiz/sorc list. However, what you get in return is powerful melee skill without having to create a complex multiclass build with PrCs and the like. You also get some VERY powerful abilities for a melee-mage that no other class gets, and while the magus may not be as strong a caster as the wizardly gish he is the BEST in the game at doing what you want: being a battle mage, so even if you would rather go the wizard/fighter/eldritch knight route I thought this class at least deserves a mention.
Don't take my words as bible, though, as I am no expert on Gishing.
you can build a straight wizard for melee... but its difficult and doesn't come together until mid to high level. if you want to try, you're on the right track- make your weapon your bonded item so you can make it brilliant energy asap (ignoring armor/nat armor will help with low BAB)... but really it'll be a long road to 11th level (when you can stack transformation with various monstrous physique spells).
if you're willing to be a bit more flexible:
magus is a good option- you probably wouldn't want to use a greataxe (since some abilities require a 1handed weapon) but you'd gain prof. with all martial weapons. reduced spell access though...
eldritch knight is the other obvious choice- if you take the divination|scryer school you can go fighter 1/wiz 1/eldritch knight; it doesn't have as much ability synergy as a magus but its only one spell level behind a full wizard and through 13th level is only 1 BAB below a fighter! (after fighter 1/wiz 2/EK 10 you have to choose how you want to divide your focus and either level wiz the rest of the way or pick up another PrC... arcane archer, dragon disciple, or hellknight signifier/enforcer are all decent options)
One of the better ways to go about this is using the SLA early entry method to Eldritch Knight with a Scryer Wizard 1/Trapper Ranger 1 (because might as well handle traps) Eldritch Knight 10/Hellknight Signifier/Enforcer 8.
This will get you 17 BAB, 18th CL (20 with Magical Knack), 9th level spells, and a host of useful abilities. Arcane Armor Training 1 and 2 each get you a -5% to Arcane Spell Failure, so combined with Mithril Armor you can wear some very good armors without needing to waste your swift action (which can then be used for Quickened Spells!).
There's some interesting alternatives like Empyreal Sorcerers with Sohei for example.
One thing to keep in mind is that in you don't get your 2 new spells if your Wizard when taking PRC levels, while Spontaneous casters do.
Also the Dimensional Dervish line of feats works quite well this allowing you to effectively Pounce (but better!) a number of times per day equal to the Dimension Doors you prep (and hey Ring of Wizardry IV is a thing).
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Yeah, I didn't really know about Hellknight Enforcer and other such things. One thing I can tell you, though, is that if you don't want to be to be a wizard and thus be forced to spend gold to get all your spells as you level through your PrCs you can qualify as a sorcerer 1/fighter 1 instead of wizard(scryer))1/fighter 1 IF you choose the default aasimiar as your race. You see, the Aasimar race gets Daylight, a level 3 spell, as an SLA and since racial SLAs always count as arcane spells unless they are only found on divine lists, you can meet the spellcasting requirement for Eldritch knight with the default Aasimair's SLA. One thing to keep in mind, though, is that ONLY the default Aasimiar qualifies. While there may be alternate heritages for Aasimiars that look better for you(like the + Str + Cha one) their SLAs are all level 2 spells rather then level 3 ones, which means they don't allow you to qualify. Only the basic, default aasimiar can allow you to do this.
Wizard overall will still be STRONGER then sorc in the long run, but sorc works out to the exact same BAB and CL as a wizard, still gets level 9 spells and also dosen't have to worry about needing gold to have any kind of magical abilities as they level up in their PrCs; they still get their spells known when taking levels of Eldritch Knight and Hellknight Enforcer/Dragon Disciple/Whatever PrC you choose.