Stasera means this evening, or tonight talking about time that you spend awake.
Stanotte means tonight but is meanly used for night time, sleeping time.
Ora and adesso used as adverbs both mean "now", no difference.
But be careful that ORA, used as a noun, can also be =hour, or =time
un'ora fa = one hour ago
il film dura due ore = the movie lasts 2 hours
che ore sono? = what's the time?
sono le 4 = it's 4.