You code would require my to do some setup of multiple dummy documents to test, so instead I'm hazarding some guesses.
For a start, you haven't used Dim oDoc as document.
Then you set oDoc to a document you open.
Then, in the For Each objShape line, you don't use the reference to oDoc, but switch to ActiveDocument. You should fix both of these problems.
When you activate the receiving document, you are using the Selection object instead of the Range object. Most likely, this is because you created the macro with the macro recorder.
The Selection object is less reliable than Range. Using Selection, it's possible you are over-writing each pasted chart with the next pasted chart. After
Selection.TypeParagraph
add
Selection.Collapse Direction:=wdCollapseEnd
to prevent that from happening.