Q. Old people have some strange habits. We must cut our nails only after a bath. is this correct?

A. It is makruh (disliked, not preferred) to clip the nails or to remove ANY hair while one is in a state of major impurity. (Fatwa Aalamgiri.) If you are not in the state in major impurity,  then it would not be makruh for you to cut your nails.

It is also good to cut the nails during the hours of the day, as opposed to the night.

In this day an age we all want proofs. Although we are glad you have shared your question with us, we must realize that older folks may not be able to give you the proof of everything. A lack of proof does not mean they lack validity in their claims. When we see that they are not violating a religious injunction, then it such a situation it would help to listen to them. However, we are just as glad to clarify such issues for you as well.

Allah certainly knows best.