"Of" does not appear to contribute to any inversion here. It is part of the noun clause, "fields of grain and trees" - specifically, it describes "fields", by telling us what kind of fields they were.
You could change the order of "fields" and "grain" without harming the meaning ("grain fields" instead of "fields of grain"), but this is not inversion in a linguistic sense.
The subject, then, is "[fields (of grain)] and [trees]". In other contexts, this might be confused with "[fields of grain] and [fields of trees]" or "fields of [grain and trees (mixed)]", but we don't normally think of "fields of trees" unless we're talking about a tree farm - a farm in which trees are grown to a size that they can be harvested for wood or transplanted elsewhere.
"Across" suggests that this is locative inversion. Note that "across" and "on the other side" are redundant, repeated for emphasis. Both of them help to describe the location, and they occur prior to the main subject/verb.
As well, note that they do not necessarily describe "along the banks of the Ebro", as "banks" is a plural form that disagrees with "side". So the larger context probably indicates that "across" and "on the other side" actually correlate to a location or object from an earlier sentence. (The previous sentence says "The girl stood up and walked to the end of the station.", which suggests that the station - or more accurately, the region around the station - is what is "across" here. If you read the entire story, the word "across" appears multiple times to refer to the valley where the station is located.)
This sentence could be rewritten in a non-inverted way as follows:
Fields of grain and trees were across, on the other side, along the banks of the Ebro.