Lying under a tree

Are all these sentences correct:

1) There was a man injured, lying under a tree.

2) There was a man injured lying under a tree.

3) There was an injured man, lying under a tree.

4) There was an injured man lying under a tree.

If they are how does the placement of 'injured' change the meaning?

I think in '1' and '2' the man was injured when he was lying under the tree.

In '3' and '4' he was injured and he was lying under a tree. We don't know where he was when he was injured.

Gratefully,

Navi