Counter Narratives (CNs) are non-negative textual responses to Hate Speech (HS) aiming at defusing online hatred and mitigating its spreading across media. Despite the recent increase in HS content posted online, research on automatic CN generation has been relatively scarce and predominantly focused on English. In this paper, we present CONAN-EUS, a new Basque and Spanish dataset for CN generation developed by means of Machine Translation (MT) and professional post-edition. Being a parallel corpus, also with respect to the original English CONAN, it allows to perform novel research on multilingual and crosslingual automatic generation of CNs. Our experiments on CN generation with mT5, a multilingual encoder-decoder model, shows that generation greatly benefits from training on post-edited data, as opposed to relying on silver MT data only. These results are confirmed by their correlation with a qualitative manual evaluation, demonstrating that manually revised training data remains crucial for the quality of the generated CNs. Furthermore, multilingual data augmentation improves results over monolingual settings for structurally similar languages such as English and Spanish, while being detrimental for Basque, a language isolate. Similar findings occur in zero-shot crosslingual evaluations, where model transfer (fine-tuning in English and generating in a different target language) outperforms fine-tuning mT5 on machine translated data for Spanish but not for Basque. This provides an interesting insight into the asymmetry in the multilinguality of generative models, a challenging topic which is still open to research. Data and code will be made publicly available upon publication.