What your grandson is doing is expressing himself in his nonverbal language. Kiddos express themselves and communicate in various ways.
He is different at school because the school environment is set up to accommodate him. It draws him in and holds his attention. Besides they are trained professionals.
You will never be in charge of spectrum behaviors. You can however jump in and try to persuade positive behaviors without kiddo knowing.
Some kids are visual learners instead of verbal. The great thing out of all this is that they have you ❤️ ♥️ 💕 and you are ready to roll up your sleeves and enter our world.

The reason he takes his clothes off is likely a sensory sensitivity to possible tags in the clothes or the fabric feels uncomfortable to him. Many ASD kids have sensitivity to various clothing textures. His hyperactive behavior is common with ASD kids, he might have ADHD which you can have him tested for. An OT can provide sensory therapy which may help regulate his sensory seeking behavior.. Look up sensory diets online, it includes activities to help him meet his sensory needs. Also look up the Wilbarger brushing protocol, this helps calm my son when he is hyperactive.
Consequences rarely work with ASD kids because they may not understand what they are doing is considered wrong. Many ASD kids struggle to understand the typical rules we have for non ASD kids. Taking away his favorite toy will usually exacerbate his behavior because he doesn’t understand why you took it away.

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27 year veteran here.
What you need to build is a 'Race-Track' for your innergenic Grandson.
What I mean by that is that you move your couch to the center of the livingroom, leaving 3 foot of clearance all the way around. That will give them a place to do Laps and burn off the energy.
Do you have anything with Lavender fragrance? If so, dilute it in a spray bottle and spray it on the couch, and on the shoulder area of their shirt. It'll help calm them down.
'Look Shiny' and 'Squirrel' are your best friends/tactics. Get some Fruit Snacks and when He starts getting excited too much for your day, break out a pack and have him sit on the couch to eat them. The distraction will at least give you some temporary relief.
These should alleviate some of the daily ASD struggle(s).

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