When you're telling stories, it's especially important if you want to be funny to use your voice to full effect. We have a whole section earlier on voices. But if you're trying to bring in humor, you really need to use your voice for maximum effect. If you're talking about a character who is clearly a different age, ethnicity, different country from you, different perspective, different accent, then try to be close to that. Now you don't want to sound like you're doing, you know, racial stereotypes and offending anyone. But if you are, for example, a young woman and you are talking about an experience, where you have this gruff old man chastising you then become a gruff, old man with your voice, no one's going to be offended by that.
Use your voice to convey the character of this person and it's okay to exaggerate slowly. No one's judging you on the standards of Are you a professional mimic, or a professional impressionist, but just bringing to life that voice with a slightly exaggerated time will make the whole thing funnier. Not every time but some of the time.