For legs you can do squats, lunges, calf raises, and many other exercises while holding dumbells.
For arms, you could do tricep curls for triceps, bicep curls for biceps, military press for shoulders, and wrist curls for forearm/wrist.
But remember that for serious upper body gains you need to do lat pull downs (upper back) and bench pressing (chest), which requires a machine and a barbell and a bench
Also, bodyweight exercises may be just as useful as dumbell exercises, try:
-Pushups for chest/shoulders
-Squats (while not holding dumbells)
-Situps
-Leg raises
-Calf raises (while not holding dumbells)
-Diamond pushups for triceps