VBA - Sorting a Table by several fields. Field names in cells (selected by user

Here's a basic example you could adapt:

Sub ListSorter()
    Dim ws As Worksheet, lo As ListObject, c As Range, noSelection As Boolean
    Dim f As String
    Set ws = ActiveSheet               'or a specific worksheet
    Set lo = ws.ListObjects("MyList")  'table to be sorted
    noSelection = True
    With lo.Sort
        .SortFields.Clear
        For Each c In ws.Range("sortfields").Cells 'loop over range with sort fields
            f = c.Value
            If Len(f) > 0 And f  "Not used" Then
                .SortFields.Add2 Key:=lo.ListColumns(f).Range, 
                                 Order:=xlAscending
                noSelection = False 'flag at least one field was chosen
            End If
        Next c
        If noSelection Then 'did the user select any sort fields?
            MsgBox "No sort field(s) selected!"
            Exit Sub
        End If
        'do the sort
        .Header = xlYes
        .MatchCase = False
        .Apply
    End With
End Sub

My example ListObject/Table and sort fields: