Looking at this poor sop a bit (and having very briefly used him), I see that Eelektross is pretty much trash on most OU teams. Good mixed attacking stats are let down by its abysmal speed stat, and while its defenses aren't terrible they aren't enough to save it either. It might have no weaknesses but its resists aren't very good either, with the only really usable one being the electric type resistance. As such, neutral attacks from any sort of attacker wreck it, and anything its actually faster than in OU is bulky enough to take its attacks and KO back.
However, as has been mentioned briefly here, I see one reprieve for this underused Pokemon. Trick Room. In trick room, it suddenly becomes a lot like Infernape, with blistering "speed" and great mixed attacking stats, losing a bit of power for a bit more defense. This means it could actually function as a decent mixed attacker / wall breaker, able to take down things like Skarmory and Jellicent while being able to 2HKO attackers that come in thanks to its decent coverage. It also has the option of running Coil, so that after Trick Room ends it can still do something.
Still, this is all theorymoning since I've never tried to use it on a trick room team (the only time I used it at all was on a terrible RMT team I was testing). It'd be worth a shot though, I think.