Nits = term for the eggs
Lice = the little dudes that run around on the scalp.

(My scalp is itching just talking about it)

As a PP said, they love clean hair, so our fave trick at childcare is to leave your conditioner in and dry your hair. Makes it look greasy and feral, but it's too slippery for them to climb up and lay eggs, so breaks the life cycle.

Vinegar - can work. I loved it as a kid.
Fine tooth comb - also works very well.
Tea tree oil - *really* works. Spray bottle with 1:100mL tea tree oil:water annoys them.

The above three will work really well as follow-up to Moov, not quite as effective on their own. You can then do all these every 4-6 weeks after your head lice case and it will help to stop recurrence.
Washing everything in hot water at the same time also helps.