First of all, I do not claim that this is the best Invoker strategy, or even that it is really all that great, but it has worked for me (in pubs) and I want to share it. This is a Mid Ganker Semi-Carry guide for Invoker which is mainly focused on maxing exort very early to get tons of spell damage early on in the game.
As stated before, this build is focused on a gank heavy invoker. As a result, we go mid in order to get that extra level and gold advantage over our enemies early game, which is extremely important for an invoker. In the ideal world, we will start to gank at a relentless pace, having a terrifying map presence, and always leaving the enemy wondering where you might strike next. If all of this goes well, you will have the levels and gold necessary to be a solid semi carry late into the game with your deadly refresher combos. However, due to BKB and increased health pools (as we are maxing exort ASAP, as far as damage goes your spells are as powerful as they will get around level 13), you will loose effectiveness as the late game progresses onward.
Starting Items: We buy the null talisman to give a boost to early game stats, particularity damage for last hitting, and the tango for some nice in lane regeneration
Early Game: The first thing we want to buy is boots of speed, because invoker's base move speed is painfully low. Then we rush out an eul's scepter of divinity. This gives us so many benefits, increased mana regen (which allows us to sustain the constant output of spells required by ganking and using sunstrike globally), movespeed (which invoker is happy to have at any time), some intelligence, and an active that allows us to execute the eul's "one shot" combo, eul's, sunstrike, chaos meteor, deafening blast. This combo will truly one shot people, hence the name. The early damage potential is truly insane, as this combo will end up dealing (including resistances) around 1200 damage, giving us our amazing ganking presence.
Core: At this point we get blink dagger for surprise initiation for the one shot combo as well as refresher combos later in the game, as well as the additional mobility. We then purchase Aghs, because it is hands down the best item on invoker as of 6.85. It reduces invoke cooldown, allowing infinitely more complex combos, gives nice stats, and makes all of our spells better (this one is really a no-brainer). After that we finish off our boots of travel, giving lots of movespeed as well as infinite map presence. Then we work on out cooldown items. Octarine core comes first, providing the constant reduction in cooldowns all around the board, helping in getting off spells more often, and the stats and spell vamp are also appreciated too. Then we buy refresher, for the ability to pull off many teamwipe combos using double chaos meteor. If you are fed enough, and they are unable to get BKB's buy the time you have refresher, you can blink in, use tornado, then emp, meteor, blast, refresh, meteor, blast to pretty much instantly kill their entire team (really. No strings attached. Sort of. You have to be fed in the first place, they cant have BKB's and you have to catch all 5 of them in a pretty timy space. Magnus and RP really helps out in this department)
Luxary: Boots of travel 2 and moon shard. If you really just have more money than you know what to do with.
We take invoke whenever possible.
We will max exort first, giving us incredible killing power early on. The level 3 point in wex is for alacrity, giving lane dominance. Use it to last hit/harass. As far as mana goes, it is free, and as far as cooldown goes, its duration is more than half the cooldown. Then we proceed to max exort, with second priority going to quas for that health regen. After that just finish up quas and wex for additional utility spellpower.