the chamois (a.k.a. "shammy") is your friend. Headliner stains can even be removed by a bit of all-purpose automotive cleaner on a chamois.
if you have access to compressed air, that, along with a detailing brush (tooth brush) will make quick work of dash/doors... great for vents and speaker grilles. Just spray the dash/door liberally with cleaner, go into any cracks with the brush, blow out the liquid with the gun, wipe clean with a cloth.
I am a detailer if you haven't guessed... I'll peak my head in again to see if there's any questions I can help with.