Over the Counter?
Over-the-counter drugs which are not expired and have been stored safely can be given away however, if in any doubt, it is safer just to throw them in the trash. Definitely do NOT give away any drugs where the package has already been opened.
When in doubt, ask your pharmacist.
Can I take drugs after they have expired?
There have been a number of studies on this and the answer is: it depends. Some tested medications remain at near full strength years after the expiry date and some find their potency highly impaired. Liquid drugs in particular do not last long including epi-pens.
Here is an article from Harvard Health that may help you understand this topic better. Please don't take random advice on this from internet strangers. Talk to your doctor.