Would this also mean "sing well", "sing forcefully", or both?
Doesn't singing forcefully mean the same thing as singing strongly?
Anyway, this does not have anything to do with singing well.
I think you could sing forcefully, with a lot of gusto and noise, but not well. Doing something "strongly" often means that you're doing it with skill.
Loudly, firmly, powerfully
Sing loudly or powerfully (but not firmly)
She can break a wine glass with her voice.