As mentioned above, nucleophilic strength does not always coincide with the strength of the corresponding base and various other factors are involved therein. But by the chance, let’s clarify the issue:
Basicity refers to the offering of the electrons pair to a proton and/or an electron cavity that leads to the formation a stable salt and/or adduct; while nucleophilicity refers to the displacement of the electrons pair in another atom (often, carbon atom) that also leads to the formation a stable salt and/or adduct. As a consequence, basicity plays an important role in nucleophilicity.
On the other hand, basicity is not affected by the steric hindrance, while nucleophilicity is highly affected by the relative size of the attacking molecule. As a consequence, the base hardness/softness also plays an important role in nucleophilicity, too.
By application of all above in the SN2 substitution, we can assume that:
1). For bases of similar hardness, nucleophilic strength follows the order of basicity strength.
OH- > Br-
2). For bases of different hardness, the softer the base the stronger the nucleophilicity is.
HS- > OH-
3). Usually, SN2 departure follows the inverse order of nucleophilicity. However, the soft base character sometimes leads to paradox behavior. As an indicative example, I- is both a soft base and a large anion and therefore, I- is both a good attacking and a good leaving group and consequently, its nucleophilicity also depends on the concentration of reactants.
For further reading, please take a look to the following or a similar textbook:
Peter Sykes: A guidebook to mechanism in organic chemistry, 6th Longman LTD, London, (1985), Chapter 4: Nucleophilic substitution at a saturated carbon atom - Subchapter 4.5: Effect of entering and leaving group, pp. 96-99