A good oil supplement is borrachio oil, under the form of capsules because it has a strong scent that might not please you so best eat it
You can try spraying some water on your face before applying your moisturizer. If water is what you lack, that helps. In terms of moisturizer you can try Hydraphase from La Roche Posay, it's good stuff. I can also suggest Weleda's almond hydrating cream.
Try using a light texture for daylight (sinks in quickly) and use a rich texture for night, night is also the time used by your skin to replenish itself so applying moisturizer at night helps that process.
You can also look for a moisturising serum, it's more concentrated than a moisturizer (you apply it before your moisturizer).
Layering is best than just applying one product, therefore applying serum, then moisturizer and even a second coat of moisturiser can work better than just moisturizer alone. It the weather is particularly windy (during winter), i apply my moisturizer regularly then apply a cream or a butter (shea butter for example) above, to act as a protection against it.
Drink water too, the trick is to drink before you feel the need to.
To wash your face, you could try oil cleansing or at least a creamy cleanser. The rest may be too drying. If that still is too harsh for you, floral water like rose or chamomile and a cotton pad can work too.
You can exfoliate very gently any dry skin flakes you might have.