If you added an equal volume of a strong alkali to a weak acid (e.g. vinegar pH=4) what pH would you expect to get?

Vinegar is basically a dilute solution of acetic acid in water.  Acetic acid has the chemical formula CH3COOH and the terminal hydrogen atom is weakly acidic.  You stated that the pH of vinegar is 4 which is in the mildly acidic realm.  If we add a solution of strong alkali (basically a strong base like NaOH), it will neutralize the acetic acid according to the chemical equation below:

CH3COOH + NaOH --> CH3COONa + H2O

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Vinegar is basically a dilute solution of acetic acid in water.  Acetic acid has the chemical formula CH3COOH and the terminal hydrogen atom is weakly acidic.  You stated that the pH of vinegar is 4 which is in the mildly acidic realm.  If we add a solution of strong alkali (basically a strong base like NaOH), it will neutralize the acetic acid according to the chemical equation below:

CH3COOH + NaOH --> CH3COONa + H2O

If by equal volumes you mean an equal number of moles of both acetic acid and alkali, then all of the acetic acid and base will be neutralized.  If the mixture were to stay like this, then the pH would be 7, or completely neutral.  But the sodium acetate conjugate base of acetic acid (CH3COONa) will establish an equilibrium with water to produce a small amount of acetic acid, thus the final pH of the resulting solution will be higher than 4 but slightly less than 7.