Firstly, which type of Eelektross suits you best - Physical or Special? Both have their pros and cons.
For a Physical Eelektross, you would want to go with:
Wild Charge
Crunch
(another move of your choice) - consider Acrobatics, Dragon Claw, Brick Break, Rock Slide
Coil
Wild Charge is a powerful physical Electric-type move, but it comes with recoil damage. Coil boosts its Attack, Defence and accuracy by one stage, so it's a useful move to have and will give you an advantage. Crunch is for variety, and you can choose any other Physical move for the last slot. You could go with Acrobatics for good strong physical damage if Eelektross is not holding an item, for example. Physical Eelektross is powerful as it uses its high Attack stat to its maximum potential, but you might want to consider Special Eelektross if you dislike recoil damage.
As for a Special Eelektross, this would be a good moveset:
Thunderbolt
Flamethrower
(another move of your choice) - consider Grass Knot, Flash Cannon, Hyper Beam
Acid Spray
Thunderbolt is, as you should know, powerful and reliable. And yes, Eelektross can learn Flamethrower! An Electric-type that can learn Flamethrower is something to look up to. Acid Spray lowers the opponent's special defence by two stages, which compliments Thunderbolt very well. The last slot is, again, up to you - I taught it Flash Cannon to deal with things Thunderbolt and Flamethrower can't hit. Special Eelektross has a slightly lower Special Attack stat as compared to its Attack stat, but it can be used well if you are able to get a Modest nature on it.
All the best and may your Eelektross be a vital member to your team! c: