Here are a few steam inhalation and massage recipes for oily skin and hair.

Steam baths for oily skin
6 dps Juniperberry Essential oil
4 dps Lemon Essential oil
4 dps Cypress Essential oil

or
2 drops Geranium Essential Oil
2 drops Grapefruit Essential Oil
2 drops Rosemary Essential Oil

or
2 drops Cypress Essential Oil
2 drops Lemon Essential Oil
2 drops Juniperberry Essential Oil

Mix these essentials oil into boiling water. Hold a towel over your head and bend over the bowl, draping the towel over the bowl so the steam does not escape.   After 5−10 minutes rinse your face with tepid − cool water and pat dry.

For Oily Hair

3 drps Ylang Ylang Essential oil
3 drps Lime Essential oil
2 drps Rosemary Essential oil
Carrier oil- 2 tablespoons
Mix all ingredients then apply 1 teaspoon to hair and scalp and massage in leaving it to soak in for several hours or overnight. Wash your hair twice with a natural unscented shampoo. Use 3 times a week. 

Oily skin massages

25ml of Carrier oil.
4 drps of Ylang Ylang essential oil
3 drops of Peppermint essential oil
3 drops of Geranium essential oil

or
3 drps Geranium Essential Oil
2 drps Lemon Essential Oil
3 drps Palmarosa Essential Oil
2 drps Rosemary Essential Oil

or
2 drps Bergamot Essential Oil
3 drps Cypress Essential Oil
2 drps Frankincense Essential Oil
3 drps Petitgrain Essential Oil

or
4 drops Geranium Essential Oil
3 drops Grapefruit Essential Oil
3 drops Lavender Essential Oil

Fractionated coconut oil and Apricot kernel oil are thinner carrier oils which are beneficial for oily skin as not to thick.

Additional info: Bergamot for oily skin blog.