The procedures for dealing with plague victims' assets most likely differed quite a lot depending on where in Europe it was. I can only speak for Scandinavia, and I assume most of what happened there happened in similar regions throughout Europe, though that could probably do with some more research from others.

Essentially, yes, survivors did just enter homes and have their pick. It all depended on where you were from; if you lived in the rural areas, for example, (which you probably did, considering the time period) there wasn't much of an authority there to establish any rules. Many abandonded farms were simply claimed by the people living nearby. In fact, one of the most widespread surnames in Scandinavia is Ødegaard, which literally means "Desolate home". People with this surname usually descend from people who occupied the abandonded properties following the Black Death.

Both in the country and in the cities, standard of living rose considerably; there was more and food available, and social mobility also became much more dynamic, however in most urban areas, it wasn't a free-for-all. To regulate who would inherit what, governments developed uses, which were documents that detaild the benefit and profit of the land. This delves more into law, which I don't know that much about, so it would be great if someone else could explain this further. In any case, uses were mostly used (pun not intended) in urban areas, and mostly concerned the estates of nobility and the upper class. In regions where the government had a far less notable presence, the process of claiming abandonded land would not have been as regulated.