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, growing out mechanical and chemical damage = breakage and very high porosity. Past armpit length heading for waist.
Treatments: Komaza protein, Komaza Matani, coconut oil with sugar syrup. Hairveda Sitrinillah
Leave in: Fructis Sleek & Shine (old), Gliss ultimate volume
Styler: Umberto Giannini jelly, Boots curl creme, Rockin RInglets
Experimenting with: Mega-Tek, Curl Harmony reviver, Elvive Full Restore 5.