Vash, shame it sounds tough.
I have read that moving house is quite traumatic for children and I think one should be sensitive for their emotions in a case like this. Your child is not naughty, but he is merely expressing his insecurities about the change. I think saying to him "No" in a stern voice would make him feel that he can't express his emotions in a safe environment. At this young age, I would rather recomend you spend some extra time with him to comfort him and reasure him that you won't leave him (this is a child's number one fear, abandonment).
When a tantrum happens, stay close to him, maybe sit next to him on the floor a meter away, and stay calm and reasure him that everything is okay and you are there to give him a hug when he is ready and calmed down. He will most likely start to move closer to you as he starts to calm down, and then hold him for a while untill he feels better.
Tantrums happen because they can't verbalise their feelings. Imagine your mouth is taped closed and you can't express your fears and frustrations about a traumatic incident in your life. We would probably all throw ourselves on the floor and start kicking! Shame, at this age, tantrums are very traumatic for them and as my therapist advised, give them your love and support and comfort.
I hope everyone settles into a new routine quickly. xx