Fireblast should be maxed first because it's the best nuke available for you. The damage if you multicast is fantastic and it's a very reliable disable. Ignite does far more damage per skill point, so consider leveling that over fireblast.

Ignite is a great second nuke available to Ogre Magi that applys a slow and some damage. It should be used after fireblast to initiate damage on an opponent. With Multicast, it becomes aoe and should be used during teamfights as much as possible. I think 2-3 levels of this early is enough.

Bloodlust is a skill that allows your carries to carry harder in the mid-late game. Unfortunately, this skill is expensive to spam in the early game so you don't pick it up until a bit later. I usually get 2-4 ignites and then max this skill out after Fireblast.

Unrefined Fireblast is granted once you have an Aghanims Scepter. The casting cost is 60% of your total mana pool, so you should use it sparingly until the fight gets serious. Always cast this immediately after you cast your first fireblast to chain stun your opponents.

Multi-cast should be gotten at all levels available because it allows you to get lucky and cast multiple fire blasts during teamfights. This can sometimes do insane amounts of damage to opponents. It also makes ignite do aoe, and bloodlust to sometimes cast on multiple heroes!

One of your support heroes should buy a Courier! If your allies don't, then you can buy ironwood branches instead.

It's extremely useful for your mid hero if there are wards covering the map and spotting out rune spots. This also protects you against early ganks.

Clarity Potions are imperative because Ogre Magi has a low int pool and requires on his casting to do damage!

You can sometimes purchase a boots at the start of the game as your base regen is high and your armor+hp are ridiculous. Only purchase boots if your other support bought a courier.

Magic stick can be left as is or upgraded depending on your game.

Flying courier should be purchased between the 2-4 minute mark by a support. Usually purchased BEFORE boots of speed.

Support heroes need to always carry a tp so that they can support other lanes when dives or ganks happen.

This is the most important item that Ogre Magi can purchase. Ogre's strength gain is one of the highest in the entire game and his int gain is quite low, which means he NEEDS an increased mana pool with mana regen. You can either buy arcanes, or purchase Tranquil + Soul Ring.

Magic Wand should be purchased on ALL support heroes! The hp and mana it gives is VERY cost effecient. If you're very poor, leave it at a magic stick until you finish Arcane boots!

Aghanims gives Ogre a SECOND fireblast nuke, which helps lock down enemy heroes. Always build this as your first major item, but don't be afraid to skip it if you have to buy wards or you're having a rough game.

Urn of Shadows is a great support item because kills will happen around you, and you can't easily afford hp regen items. Urn also provides you important hp and mana regen. Make sure there is only 1 urn per team though!

Force staff is an all around fantastic item on ANY support hero because you can use it to save allies and yourself, as well as get into position to disable enemies. The extra int and hp regen doesn't hurt either.

Blink dagger is another useful mobility item that you can purcahse as an Ogre. I recommend getting 1 of the 2 mobility items and then making Aghanims, or rushing straight for Aghs.

Tranquil Boots + Soul Ring can be purchased as an alternative for Arcane Boots if you are roaming a lot. Generally Arcanes is better for your team though.

Ghost scepter is often a fantastic item to keep supports alive versus physical damage carries such as Anti Mage or Lifestealer. The bonus stats are really useful as well.

If the enemy team has an invisible hero then a support should purchase the gem. This could be you!

Veil can be great for Ogre Magi because most of his damage is magic, and it gives him armor, hp regen, and more mana for spells! Very easy build up as well that can situationally be useful.

Ogre is one of the few support heroes who is melee, so a stout shield goes a long way in the early game towards giving him survivability. Consider picking one up if you random!

Mek CAN be gotten but I wouldn't make it your main focus. DO NOT pick it up unless you have arcane boots, as you won't be able to support the mana costs!