Wolverine gets affected as any other human being by electricity. Of course, having his skeleton covered in a conductive metal won't help to bear it.
However, you must remember that the main power of Wolverine is to regenerate in an overwhelming way from any cellular damage he receives.
Electricity can cause different kinds of damage to human beings:
- It burns the skin, flesh and even bone if enough voltage is applied.
- It can shatter also skin, flesh and bone depending on the shock, however this is less frequent
- It can cause severe damage to the neuronal system, literally burning the nerves and even the brain.
Wolverine can quickly regenerate any type of damage to his skin, flesh, bone or neuronal system, so the answer to your question is:
Yes, it affects him.
Yes, it affects him in a greater way than a normal human.
No, it doesn't have any permanent harmful effect to him greater than other harmful events, like firearm shots, fire or acid.
BONUS: His skeleton makes him extremely vulnerable to magnetism (which is closely related to electricity), as our loved hero/villain Magneto had the opportunity to test on multiple occasions.