Newb here.

I want to change my string from 9's to 10's on my Squier Strat. However this time, I'm gonna tune it to Eb.

The question is, do I need to adjust something on my guitar? Truss rud adjustment, or Intonation?
You'll only find out what you need to do after you change the strings and tune it up.
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Doubt it. Maybe the slightest action and intonation tweaks.
Charvel / Godin / Peavey / Marshall / AMT
I've done exactly the same thing once, it was all fine, no truss rod adjustment was needed, everything was OK. String tension is going to be almost the same, it's not a big change.
Should be fine. If you'll go for larger gauge, like .11, you may need to enlarge nut slots.