You had it almost right the first time, but you need to set the last row e.g. as follows. You also need to set the numeric values of the Word commands or they won't work with late binding. You haven't defined all your variables.
Code:
Option Explicit
Sub Export()
Dim wdApp As Object
Dim wd As Object
Dim xlSheet As Worksheet
Dim rng As Range
Dim LastRow As Long
Const wdReplaceAll As Long = 2
Const wdFindContinue As Long = 1
On Error Resume Next
Set wdApp = GetObject(, "Word.Application")
If Err.Number <> 0 Then
Set wdApp = CreateObject("Word.Application")
End If
On Error GoTo 0
Set wd = wdApp.Documents.Add
wdApp.Visible = True
Set xlSheet = ActiveWorkbook.Sheets("INV")
With xlSheet
LastRow = .Cells(.Rows.Count, "A").End(xlUp).Row
Set rng = .Range("A1:D" & LastRow)
rng.Copy
With wd.Range
.Collapse Direction:=1
.InsertParagraphAfter
.PasteSpecial DataType:=1
With .Find
.ClearFormatting
.Text = vbTab
.Replacement.ClearFormatting
.Replacement.Text = " "
.Execute Replace:=wdReplaceAll, Forward:=True, Wrap:=wdFindContinue
End With
End With
End With
End Sub