of course = yes; a strong yes. Similar to "certainly."
Woman: Do you love me?
Man: Of course, I do! Give me a kiss!
off and on = not a regular schedule; temporary; similar to "sometimes."
He’s been sleeping off and on while trying to finish a big project.
He works off and on for a software company.
on the other hand = however; but. Used for showing contrast
Visiting China for the Olympics this year would be fun; on the other hand, it might be really expensive. We should wait until next year.
on the dot = exactly on time
Ms. Johnson expects her employees to arrive at work every morning on the dot–or earlier.
on time = not late; not too early.
Blake wasn’t on time for his date with Stephanie, so he brought her some flowers.
In fact, he’s never on time.
once again = another time; once more.
Once again, he’s hurt his back by trying to lift something heavy. His wife keeps telling him not to even try.
open to = ready to accept new ideas.
It’s a wise person who is open to new ideas.
Are you open to learning new things?
("Open to" can be followed by a gerund. In the example above, "learning" is a gerund.)