Despite the rapid recent progress in creating accurate and compact in-context learners, most recent work focuses on in-context learning (ICL) for tasks in English. However, the ability to interact with users of languages outside English presents a great potential for broadening the applicability of language technologies to non-English speakers. In this work, we collect the infrastructure necessary for training and evaluation of ICL in a selection of Slavic languages: Czech, Polish, and Russian. We link a diverse set of datasets and cast these into a unified instructional format through a set of transformations and newly-crafted templates written purely in target languages. Using the newly-curated dataset, we evaluate a set of the most recent in-context learners and compare their results to the supervised baselines. Finally, we train, evaluate and publish a set of in-context learning models that we train on the collected resources and compare their performance to previous work. We find that ICL models tuned in English are also able to learn some tasks from non-English contexts, but multilingual instruction fine-tuning consistently improves the ICL ability. We also find that the massive multitask training can be outperformed by single-task training in the target language, uncovering the potential for specializing in-context learners to the language(s) of their application.