Invasion? What Invasion?

Garrison Invasions are challenges in your Garrison that allow you to defeat attacking enemies for rewards.
They can be completed solo but you are encouraged to bring your friends because the rewards are greater if you perform better.
Your first invasion comes early on Shadowmoon Valley and Frostfire Ridge with a Tier 2 Garrison--midway through questing, a player's Garrison will be attacked either by a Thunderlord or Shadowmoon force. This is not available with a Tier 3 Garrison but it is also not considered a "real" invasion.

There are 6 types of invasion:
Ogre
Shadow Concul
Shadowmoon
Botani
Goren
Iron Horde

HOW TO TRIGGER AN INVASION
When you kill level 100 mobs (in the areas for Apexis Crystal Quests), you have a chance that the enemies will prepare to attack your garrison in retaliation. At this point, your commander by the Town Hall will have a quest for you.

In order to trigger an invasion, you will need to kill mobs at following locations:
http://i.imgur.com/RVKLBzR.jpg

Note that you need to kill approx 500 mobs, and you can not be in the raid group. Party is allowed.
Once you kill enough of them, you will get notification at your minimap, where you can see mission status. There will also be big yellow exclamation mark there, pretty easy to spot. Once you spot it, head back to your garrison and you will be able to take quest from Sergeant Crowler (A) or Sergeant Grimjaw (H).

Invasion Stages
The invasion has the following stages:
Invasion - Follow the sergeant
Assault - defeat the assault.
The holdout - endure the assault. This part is timed for ~8 minutes.
The calm - go to the town center
Final stage - kill a boss

During the assault, multiple enemy packs spawn in your Garrison.The following unusual things can happen as well:
The enemy assaults a Garrison building—attack them to interrupt the cast.
A terrified townsfolk runs out of safety. They are marked with a green arrow over their head and you run up to them to move them away.
An infiltrator from the opposite faction is in your Garrison. These have a hefty bit of HP.

Invasion Points
During the invasion, you gain points via the following ways:
Killing enemies—trickier ones give more points.
Saving terrified townsfolk.
Killing spies.
Keeping your buildings intact.
Keeping your defenders alive.
Killing the final boss.
When the invasion is complete, points are added for your buildings and defenders.

You need 300 points for Bronze, 600 for Silver, and 1000 for Gold.

Invasion rewards
Silver and bronze rankings rewards only apexis crystals, but if you managed to get gold reward you will get Invader's Forgotten Treasure which can contain 645 items (They can be warforged 651) and one of 4 mounts.
Note that you can get each bag just once per week, yet you will receive apexis each time you do it.

Good luck with invasions!

This is still very much doable and because of your garrison grunts are now 110, they will kill the mobs alone and you can afk most of the invasions (Shadowmoon Invasion being the only exception) out as it doesnt matter which rank you get out of them. You can purchase and complete as many assaults in a day as you wish from the Garrison Quartermaster and they will all grant an invasion immediately.

I tested all the assaults to bank up invasion quests and below is my findings on a max level mage ice lancing everything: (also killing boss's if they were up which they should be on most servers)
ogres - assault on stonefury cliffs - 1min50s
ogres - assault on the ring of blood - mission was not available

goren - assault on magnarok - 50s
goren - assault on broken precipe - 1min

iron horde - assault on iron siegeworks - 1m50s
iron horde - assault on the pit - 40s with or without bosses aoe'ing the pit
iron horde - assault on mok'gol watchpost - 90s

shadowmoon - assault on pillars of fate - 1m50s
shadowmoon - assault on skettis - just dont do this one its horrendous and gave an annoying combat lock
shadowmoon - assault on darktide roost - 3min
shadowmoon - assault on socrethars rise - 45s focusing boss's

botani - assault on the everbloom wilds - 90s focusing hydras for 5% each
botani - assault on lost veil anzu - 2m45s and gave an annoying combat lock

shadow council - assault on shattrath harbor - 2min20s
shadow council - assault on the heart of shattrath - 90s focus rares

Based off the above the best route is:
Assault on Stonefury Cliffs (ogres)
Assault on Magnarok (goren)
Assault on The Pit (iron horde)
Assault on Everybloom Wilds (botani)
Assault on Socrethars Rise (shadowmoon)
Assault on Heart of Shattrath (shadow council)

You don't need to do all the other meh assaults.

That will give you your 6 invasion quests the fastest. (from personal experience)
I use this method every 6 weeks as I do 1 invasion per week for the loot/mount chances.