What does 'across the level' mean here, and 'striking off across' mean
With a short laugh he threw it down on the bed, and pulling on his old black hat, he went out, striking off across the level.
On the Divide by Willa Cather
The word "level" appears four times in that story. The first appearance is at the beginning, where it appears in the first sentence "... the level Nebraska plain...".
In the sentence you quote, it means that he walked across the land, which is very flat.