(Not a Teacher)
Since I have no shame, I'll answer you're question with unflinching candidness.
These terms can have a variety of meanings depending on the context, but in terms of sex:
"Nailed" is almost exclusively used by males:
"I nailed Jennifer after the prom."
"F*cked" can be used by either gender:
"I heard Samantha f*cked him in the locker room."
"The football team captain got caught f*cking the principal's daughter."
"Screwed" is like nailed, in that it's mostly used by males:
"He screwed her all night long."
Student or Learner