The acids are the easy part...
there are 3 hydrohalic acids that are strong acids that you should just memorize: HCl, HBr, and HI....(HF is a weak Hydrohalic acid.)
The Oxoacids are strong acids in which the O atoms exceed the number of ionizable protons by two or more. Ex: HNO3, H2SO4, HClO4...remember this rule and you'll spot them right away.
Strong bases require a little more knowledge of solubility...
Strong bases are water soluble compounds containing O2- or OH- ions.
This would include group 1A metals such as Li, Na, K, Rb, and Cs
EX: LiOH, NaOH, KOH
Also includes 2A metals such as Ca, Sr, Ba...each of which combines with O2- or (OH)2
good luck.