"slå" in this context means "mow with a scythe".hmmm... I think "barn" implies a place in which you store things, like animals or what you harvest. "Koja" on the other hand to me seems more like a place in which people are, and it's also as you thought generally smaller. I'd also say it's more basic than a home of course.
So in this case I'd say that this is a structure similar to a "cabin", basically equipped, and used during the time that people are engaging in "slåtter". "slåtter" is translated into "mowing", though I think it's a bit more specific and relates to traditional mowing when managing larger or specific areas especially in agriculture.
I hope that's an accurate description and I think other Swedes can fill in the gaps or correct me. Anyway, if you search for the respective words separately you'll likely find descriptions of both. And actually, "slåtter" is perhaps best understood by looking at what you find on YouTube when searching on that term.