Our four month old boy seems to get fussy at times and starts shaking his arms, startles easy and makes nervous, jittery like movements. Normal?

Doctor can evaluate. Jittery or shaky movements in a startled 4-month old baby may be normal, but it is hard to tell without examining the baby and seeing the movements. The best way to do this is to make videos of the baby's movements and show the pediatrician, who can take into consideration the progress in all the areas of baby development, before deciding whether the baby's movements are normal for his age.
Baby tantrums. It is still normal for a 4 month old to startle easily and make jittery movements. This will normally resolve in time, about 6 months old. If it goes beyond this age, may need to be evaluated for other causes.
See pediatrician. I would consult your pediatrician. You may find that this occurs before feeding time. Keep track of the time this happens related to other factors such as meals, nap time or whether you child is constipated.