Learning about Sensory Integration because of my special needs child Aidan has been very useful for me -- I wish I had known more about it before because I think I would have understood my older children better. Some of the things that looked like personality quirks or learning difficulties might have been partly related to sensory needs that I could have addressed more intentionally.
As a toddler, in certain situations, Aidan used to become tenser and tenser and finally go into "meltdown" mode or even "blinded by stimulus" mode where he would rush around like a chicken with its head cut off. I eventually learned that if I hugged him and then tilted him upside down for a few moments it helped him immensely to stabilize. Jumping on a trampoline with him helped too.
Paddy has a tendency to get overstimulated too. They call a need for sensory input "sensory seeking" -- but I've noticed that with my kids, at least, they often need extra physical input when they are visually or auditorially overstimulated. So it seems to be a balance they crave. After watching his siblings playing an exciting video game, Paddy will often have a soaking wet sleeve because he has been chewing on it absentmindedly the whole time. When he has been sitting for a long time doing school or listening to a story or watching a video -- where his vision and mind is activated but his body has been still -- he'll often start jostling his siblings or pick a battle with one of them.
For these types of reasons, it's very useful to have a chart like this one accessible. Paddy loves interaction and games so we play a "battle" game. We take turns calling out the name of the battle -- "The Hugging Battle!" "The Squeezing Battle!" "The Back-Patting Battle" "The Light Saber Battle". The point is that it is physical and friendly (except that Paddy insists on winning) and helps stabilize his sensory system.
Here's another list of possible activities. Every child is different, so it takes some trial and error to find things that work. One of my older kids was sensory avoidant -- certain textures, sounds and smells drove him crazy -- so what works for my younger two would have caused stress for him.