I don't think there is much difference between the first two words. While writing this I couldn't come up with a case where they couldn't be interchanged...

With regards to the second pair, these words are quite different. Футляр is a case designed for storing and/or carrying around a particular item, e.g. футляр для очков, футляр для скрипки, etc. Контейнер is just a container, a much more generic type of packaging. It could be a 19" sea container or a small egg container. However, it is more likely to be something big in Russian...