Who diagnosed your son OP?
Treatment for SPD used to be available on the NHS. My DD was diagnosed with what's now called SPD (thankfully changed from Sensory Integration Dysfunction and then something else I can't remember) by the NHS Paediatric Sensory OT over 15 years ago.
They lent me A.Jean Ayres' book 'Sensory Integration and the Child ' to read as there wasn't much info around then. It certainly explained a lot about my DD's behaviour that had been puzzling me for years and the interventions and exercises that the OT tailor-made for both home and school were definitely very helpful.
My DD is an adult and has in no way grown out of her SPD, despite interventions, she still cannot do any of the things that ketchupthebear's son can as outlined above, nor can she do a lot of others like run, walk up or down steps with no handrail, judge distances between herself and another person or object.
However, maturity, being female, her own masking skills and social convention have taught her not to visibly react in the same way she did when she was a young child wherever possible, so a casual observer may think she's grown out of some of the sensory issues she displayed as a child.
Back to the OP All of his behaviours are localised to the nursery environment where he gets very amped up and excited and cant bring himself back into a state of calm. It prevents him from being able to listen or concentrate properly
There are lots of things you can do at home for this, knobbly cushions give proprioceptive feedback whilst the task is ongoing. If that's not enough, give him a 'job' to do whilst carrying a rucksack with a few books in it before he's expected to sit still and pay attention.
Have a look online for interventions, try any of the suggestions that will not cause harm, even if they sound a bit odd and see what works for your son. every child is different. Also see if any of the interventions for ADD will help.
If you've made absolutely no progress after a few months, then do consider getting specialist OT help. If you find the cost is excessive, then if your son is eligible for DLA that should help.