I believe the code you have above is missing the 'FROM MechanicalData' clause. Using the suggestions from above, the following should work (assuming all combobox values are non-numeric):
Dim strWhere As String
strWhere = " WHERE (1=1)"
If Not IsNull(Axis.Value) Then strWhere = strWhere & " AND ([MechanicalData.Axis] = '" & Axis.Value & "') "
If Not IsNull(TestType.Value) Then strWhere = strWhere & " AND ([MechanicalData.Test Type] = '" & TestType.Value & "') "
If Not IsNull(Temperature.Value) Then strWhere = strWhere & " AND ([MechanicalData.Temperature] = '" & Temperature.Value & "') "
If Not IsNull(BilletNumber.Value) Then strWhere = strWhere & " AND ([MechanicalData.Billet Number] = '" & BilletNumber.Value & "') "
If Not IsNull(BilletMaterial.Value) Then strWhere = strWhere & " AND ([MechanicalData.Billet Material] = '" & BilletMaterial.Value & "') "
Me.DataView.RowSource = "SELECT [Billet Material],[Billet Number], " & _
"[Specimen],[Temperature],[Modulus],[Ultimate Tensile Strength],[Strain] " & _
"From MechanicalData " & _
strWhere