If you strip too much facial oil, does moisturizer solve the problem? Will it be fine?

Like if your skin is super dry and flaky-ish, then yeah.

You'd be best off using a light, non-comedogenic (doesn't clog pores) moisturizer.

Yah you want to stay away from products that really strip away too much facial oil. [example: Stridex pads]. Your skin basically freaks out, and starts producing more sebum and oil to keep it moisturized. So I would stick to cleansers and light good quailty astringents.
Yes, a good moisterizer is crucial! Make sure it is light and good for your skin type. I have dry and oily patches on my skin, and I use "Balanced Diet" from Origins. That stuff works wonders.