I understand if you have a protic solvent, it will stabilize the strong base (to form weak acid) or the strong nucleophile. The protons would react with them. To have an SN2 or an E2, so you need an aprotic solvent. I also know that in general, a tertiary substrate will favor SN1/E1 reactions, because a tertiary carbocation is more stable. A primary substrate will SN2/E2 reactions, because of less stereo-hinderance.
But why does SN2 favor strong nucleophile and SN1 favor weak nucleophile from the first place? Besides, does E2 favor a strong base, and E1 favor a weak base? I also don't get the reason.