Squirming all night

My 4mth + 3 weeks old is "sleeping" for a longer stretch at night (6hrs), but he squirms around, kicks his legs up, tosses from side to side and sucks on his hands. Definitely not what I would call restful sleep. We let him be until he starts to cry. That's when I change and feed him.

He's been quite cranky (over tired) the last 2 days, so I'm wondering if this type of sleep is normal, or should we be doing something different.

Obviously the holidays didnt help- he was up late for 4 days and it totally did a number on his sleeping routine (usually was in bed by 8pm, sleeping. But only got to bed at around midnight most nights).