I personally don't usually care about nature,
when leveling up, I would recommend giving your Eelektross the power lens, due to its already poor speed.
Thunder- I think a very good move, and it gets STAB. Becasue it has more PP than blizzard, it doesn't matter quite as much, but it is a problem due to, again, Eelektross's bad speed.
Flamethrower/Thunderbolt- Honestly, I just love flamethrower as a move, and allows you to remove several types that you before could not quite as quickly, and with a low-speed like Eelektross, every turn counts. Both have 95 power and 100 accuracy, but thunderbolt has STAB, and each have their own special effects.
Flash cannon- In case of a rock type (Boldore) with smack down, You can take advantage of its even worse speed to smash it up with flash cannon, a steel move. Problem is probably going to be sturdy, but i'm sure you'll think of something.
Crunch- Just a nutarally learned move that I think will consistantly come in handy, especially if you plan to train against the elite four.