You cannot copy content from a document without opening it. That said, you could hide the documents being opened by changing:
Set oDoc = Documents.Open(strPath & strFilename)
to:
Set oDoc = Documents.Open(strPath & strFilename, False, True, False, , , , , , , , False)

The reason for only the last document's content displaying is that the code needs to have something like:
oRng2.InsertAfter vbCr
oRng2.Collapse wdCollapseEnd
inserted after:
oRng2.Text = oRng.Paragraphs(1).Range.Text

__________________
Cheers,
Paul Edstein
[Fmr MS MVP - Word]