It's not always true that a strong acid reacting with a strong base at equivalence point will always give you a pH of 7. It all depends on the ions that are left over after the reaction that reacts with the vast amount of water that determines the final pH.

THe acidity constant (Ka) of the strong acids and bases makes sure that when you react them, there will be a very miniscule amount of the original acid or base left, but you are left with the conjugate of it. Now depending on the conjugate, which also has an acidity constant, if it has a stronger Ka then H2O then it will react with the water and change the pH. Strong acids and bases usually have weak conjugates, meaning low Ka values for the conjugates, and hence won't react with the water to change the pH.

Weak acids and bases on the other hand are different, since now you are working with an equilibrium reaction instead. Even if you reach the equivalence point, if you do let the reaction rest for a while the reaction will try to reach equilibrium. By reacting a strong acid/base to a weak base/acid, you're just disturbing an equilibrium reaction. The conjugate ion of the weak acid/base is actually has a much stronger Ka value to H2O and hence reacts to the water to determine the new pH. Basically they act as buffered solutions and so they will always try to reach their equilibrium point with the pH of the solution being the conjugate ion that predominates more.

Hope this help!