As I said in your other thread, baking soda is highly alkaline and damaging to both skin and hair, more so than even sulphate shampoo. Baking soda should remove oil if you use enough, it saponifies natural oils (turns them to soap). Baking soda is a chemical BTW it is sodium bicarbonate, chemical formula NaHCO3.

Conditioner only washing removes excess oil very effectively. If you want something edible as well as kind to hair you might try mixing either egg or honey with your oil to see if that helps it rinse away.
2a-2c, medium texture, porous/ colour treated. Three years CG. Past bra strap length heading for waist.

CO-wash: Inecto coconut/ Elvive Volume Collagen
Treatments: Komaza Care Matani, coconut/ sweet almond/ fractionated coconut oils, Hairveda Sitrinillah
Leave in: Fructis Sleek & Shine (old), Gliss Ultimate Volume, various Elvive
Styler: Umberto Giannini jelly, Au Naturale styling gelee
Flour sack towel, pixie diffuse or air dry.
Experimenting with: benign neglect