I often post jokes on my social media accounts. They are read by both men and women. Am I doing something haram if a woman reads it and laughs?
Also if some woman texts me saying something funny related to the jokes, replying her would be haram as well?

In the first case, no it would not be forbidden.
In the second case, it is questionable, it is forbidden if it will lead into sin. It’s better to avoid such a thing.