Can I ask why you are adjusting the action height when you are trying to sort out the intonation?
Before you adjust the intonation you should:
1) set the action to a suitable height.
2) adjust the truss rod to provide at least a business card's clearance beneath the high E string at the frets between 11 and 13, with the string fretted at the top fret usually 22 on a Strat.
3) tune the guitar. With the tuner still plugged in make sure that when you fret each string at the 12th fret the pitch of the string does not change (this is easiest done by playing an octave harmonic and then fretting the string). The intonation is adjusted by moving the bridge saddle towards the neck if the fretted note is too low, or towards the tail piece if too high, and NOT by adjusting the bridge height.
That said, a friend of mine has a cheap Strat that will not intonate properly no matter what.
Try these helpful vids:
I set up all my guitars using his advice - and they are all jolly good now, even the cheapest one.