Short circuiting logical expressions?

I can't tell what you're trying to do. Maybe this:

Sub Calculate_phase()
    Dim i   As Long    'variable for looping in the for loop
    Dim w   As Long
    
    w = 8

    For i = w To 1 Step -1

        Application.Goto ActiveWorkbook.Sheets("Sheet1").Range("P2")

        If ActiveCell.Offset(i - 1, 2) <> "" Then
            If DateValue(ActiveCell.Offset(i - 1, 2)) < Date Then
                ActiveCell.Offset(i - 1, -7).Value = "4"
            End If

        ElseIf ActiveCell.Offset(i - 1, 1) <> "" Then
            If DateValue(ActiveCell.Offset(i - 1, 1)) < Date Then
                ActiveCell.Offset(i - 1, -7).Value = "3"
            End If

        ElseIf ActiveCell.Offset(i - 1, 0) <> "" Then
            If DateValue(ActiveCell.Offset(i - 1, 0)) < Date Then
                ActiveCell.Offset(i - 1, -7).Value = "2"
            Else
                ActiveCell.Offset(i - 1, -7).Value = "1"
            End If
        End If
    Next i
End Sub

Also, if the cells in question contain actual dates (as opposed to text that looks like dates), I'd change the coode to look more like this:

Sub Calculate_phase()
    Dim i       As Long
    Dim w       As Long

    w = 8

    For i = w To 1 Step -1
        Application.Goto ActiveWorkbook.Sheets("Sheet1").Range("P2")

        With ActiveCell
            If .Offset(i - 1, 2).Value <> "" Then
                If .Offset(i - 1, 2).Value < Date Then
                    .Offset(i - 1, -7).Value = "4"
                End If

            ElseIf .Offset(i - 1, 1).Value <> "" Then
                If .Offset(i - 1, 1).Value < Date Then
                    .Offset(i - 1, -7).Value = "3"
                End If

            ElseIf .Offset(i - 1, 0).Value <> "" Then
                If .Offset(i - 1, 0).Value < Date Then
                    .Offset(i - 1, -7).Value = "2"
                Else
                    .Offset(i - 1, -7).Value = "1"
                End If
            End If
        End With
    Next i
End Sub