We demonstrate, in this study, that an open-domain conversational system trained on idioms or figurative language generates more fitting responses to prompts containing idioms. Idioms are part of everyday speech in many languages, across many cultures, but they pose a great challenge for many Natural Language Processing (NLP) systems that involve tasks such as Information Retrieval (IR) and Machine Translation (MT), besides conversational AI. We utilize the Potential Idiomatic Expression (PIE)-English idioms corpus for the two tasks that we investigate: classification and conversation generation. We achieve state-of-the-art (SoTA) result of 98% macro F1 score on the classification task by using the SoTA T5 model. We experiment with three instances of the SoTA dialogue model, Dialogue Generative Pre-trained Transformer (DialoGPT), for conversation generation. Their performances are evaluated using the automatic metric perplexity and human evaluation. The results show that the model trained on the idiom corpus generates more fitting responses to prompts containing idioms 71.9% of the time, compared to a similar model not trained on the idioms corpus. We contribute the model checkpoint/demo and code on the HuggingFace hub for public access.