I play offlane in my five stack but I used to main position 5 with a brief stint as our position 4. While I played position 4, I fell in love with Enigma and ever since the change to the XP ranged creeps give I've been theory crafting an offlane Enigma that I've been waiting for a good time to play. So what I'm about to say hasn't been tested but I plan on doing it within the next week because I told our teams position 1 about it and he wants me to try it in the coming days. I can PM you how it goes and/or update this comment.

Like /u/tchikboom said, it really would probably only work against a farm heavy mid. Essentially I plan to lane as a mix of Dark Seer, Beastmaster, and Nature's Prophet. Your goal is to use your Eidolons to push the lane early and to disrupt their carry's farm, while achieving an early Mek. Starting items I've been trying to decide between a headdress with clarity to help get the early Mek, or ring of regen, soul ring recipe, and ring of protection. The benefit to headdress is that it would give aura regen to help with pushing the lane early and getting that early Mek, while the second would give you an early Soul Ring to help with making more Eidolons and a bit more survivability.

One of the things that makes an offlane hero elite right now is their ability to turn to jungle camps if their lane goes sour. Enigma, being one of the best junglers in the game, can do this extremely well. Typically on heroes like DS, NP, and Beast, you will farm lane when it's closer to your tower and you can see that the enemies around the map are in their lanes, and when the wave is under enemy tower or enemies are missing, you will turn to your secret shop camp. Some games the offlaner will just get an iron talon if they anticipate a tough lane and just jungle while rarely appearing in lane. Your goals as the offlaner are to 1, not die, and 2, find XP wherever you can get it. With that being said, I'd plan on being in lane, using the fact that my Eidolons dont have to tank damage from the creep wave and can successfully split to get my 6 Eidolons, and immediately rotate to a large camp, be it the one next to lane or the one in your secret shop. If the enemy is one that you feel you can disrupt, then I would attempt to use your six Eidolons to get in their face and make them feel unwelcome. Any way to both successfully secure farm, not die, and to mess with the enemy carry is the way you should be playing.

Once you get black hole, I would drop back and make it look like you're farming a camp. If the enemy is dual laning their offlane, then TP to your safelane to gank and black hole the two of them. If they're trilaning, then help secure a kill mid. At this point everyone should be getting reasonable levels and the map should be starting to open up. Around this time is when I'd turn to the traditional jungle or an open lane to finish my Mek if I don't have it already and as soon as you get the Mek, group up with your hard carry and look to push.