[Browsable(false)]
public IComparer QualitativeScaleComparer { get; set; }

<Browsable(False)>
Public Property QualitativeScaleComparer As IComparer

using System;
using System.Collections;

namespace QualitativeScaleCustomSortOrderSample {
    class NumberComparer : IComparer {
        public int Compare(object x, object y) {
            int iX = NumberConverter.ToInt(x);
            int iY = NumberConverter.ToInt(y);
            return iX - iY;
        }
    }

    class NumberConverter {
        public static int ToInt(object o) {
            string stringNumber = o as string;
            int number = 0;
            if (stringNumber == null) return -1;
            if (Int32.TryParse(stringNumber, out number))
                return number;
            switch (stringNumber.ToLower()) {
                case "one": return 1;
                case "two": return 2;
                case "three": return 3;
            }
            return number;
        }
    }
}

Imports System
Imports System.Collections

Namespace QualitativeScaleCustomSortOrderSample
    Friend Class NumberComparer
        Implements IComparer

        Public Function Compare(ByVal x As Object, ByVal y As Object) As Integer Implements IComparer.Compare
            Dim iX As Integer = NumberConverter.ToInt(x)
            Dim iY As Integer = NumberConverter.ToInt(y)
            Return iX - iY
        End Function
    End Class

    Friend Class NumberConverter
        Public Shared Function ToInt(ByVal o As Object) As Integer
            Dim stringNumber As String = TryCast(o, String)
            Dim number As Integer = 0
            If stringNumber Is Nothing Then
                Return -1
            End If
            If Int32.TryParse(stringNumber, number) Then
                Return number
            End If
            Select Case stringNumber.ToLower()
                Case "one"
                    Return 1
                Case "two"
                    Return 2
                Case "three"
                    Return 3
            End Select
            Return number
        End Function
    End Class
End Namespace

private void OnLoad(object sender, EventArgs e) {
    XYDiagram diagram = chart.Diagram as XYDiagram;
    if (diagram == null) return;
    diagram.AxisX.QualitativeScaleComparer = new NumberComparer();
}

Private Overloads Sub OnLoad(ByVal sender As Object, ByVal e As EventArgs) Handles MyBase.Load
    Dim diagram As XYDiagram = TryCast(chart.Diagram, XYDiagram)
    If diagram Is Nothing Then
        Return
    End If
    diagram.AxisX.QualitativeScaleComparer = New NumberComparer()
End Sub

private void Form1_Load(System.Object sender, System.EventArgs e){
  chartNewCusts.SeriesTemplate.ValueScaleType = ScaleType.Numerical;
  chartNewCusts.SeriesTemplate.LegendTextPattern = "{V:n}";
  chartNewCusts.SeriesTemplate.CrosshairLabelPattern = "{S} : {V}";
  chartNewCusts.SeriesTemplate.Label.EnableAntialiasing = DevExpress.Utils.DefaultBoolean.True;
  chartNewCusts.SeriesTemplate.Label.Shadow.Visible = false;
  chartNewCusts.SeriesTemplate.Label.TextColor = Color.Black;
  chartNewCusts.SeriesTemplate.Label.ResolveOverlappingMode = ResolveOverlappingMode.HideOverlapped;
  chartNewCusts.SeriesTemplate.LabelsVisibility = DevExpress.Utils.DefaultBoolean.True;
  chartNewCusts.SeriesTemplate.Label.TextPattern = "{V:n0}";
  chartNewCusts.DataSource = GetSales();
  chartNewCusts.SeriesSorting = SortingMode.Ascending;
  chartNewCusts.SeriesDataMember = "GroupField";
  chartNewCusts.SeriesTemplate.ArgumentDataMember = "MonthYear";
  chartNewCusts.SeriesTemplate.ValueDataMembers.AddRange(new string[] { "NewCustCount" });
  XYDiagram diagram = chartNewCusts.Diagram as XYDiagram;
  if (diagram == null)
      return;
  diagram.AxisX.QualitativeScaleComparer = new CaseInsensitiveComparer();
  try{
    (XYDiagram)chartNewCusts.Diagram.AxisY.Label.TextPattern = "{V:n0}";
    (XYDiagram)chartNewCusts.Diagram.AxisY.Label.EnableAntialiasing = DevExpress.Utils.DefaultBoolean.True;
    (XYDiagram)chartNewCusts.Diagram.AxisX.Label.EnableAntialiasing = DevExpress.Utils.DefaultBoolean.True;
  }
  catch (Exception ex){
  }
}

private DataTable GetSales(){
  DataTable table = new DataTable("Sample");

  table.Columns.Add("MonthYear", typeof(string));
  table.Columns.Add("GroupField", typeof(string));
  table.Columns.Add("NewCustCount", typeof(int));

  DataRow row;

  row = table.NewRow();
  row("MonthYear") = "01-2015";
  row("GroupField") = "Customer Referral";
  row("NewCustCount") = 1;
  table.Rows.Add(row);

  row = table.NewRow();
  row("MonthYear") = "01-2015";
  row("GroupField") = "Walk-In";
  row("NewCustCount") = 1;
  table.Rows.Add(row);

  //...

  return table;
}

Private Sub Form1_Load(sender As System.Object, e As System.EventArgs) Handles MyBase.Load
    chartNewCusts.SeriesTemplate.ValueScaleType = ScaleType.Numerical
    chartNewCusts.SeriesTemplate.LegendTextPattern = "{V:n}"
    chartNewCusts.SeriesTemplate.CrosshairLabelPattern = "{S} : {V}"
    chartNewCusts.SeriesTemplate.Label.EnableAntialiasing = DevExpress.Utils.DefaultBoolean.True
    chartNewCusts.SeriesTemplate.Label.Shadow.Visible = False
    chartNewCusts.SeriesTemplate.Label.TextColor = Color.Black
    chartNewCusts.SeriesTemplate.Label.ResolveOverlappingMode = ResolveOverlappingMode.HideOverlapped
    chartNewCusts.SeriesTemplate.LabelsVisibility = DevExpress.Utils.DefaultBoolean.True
    chartNewCusts.SeriesTemplate.Label.TextPattern = "{V:n0}"
    chartNewCusts.DataSource = GetSales()
    chartNewCusts.SeriesSorting = SortingMode.Ascending
    chartNewCusts.SeriesDataMember = "GroupField"
    chartNewCusts.SeriesTemplate.ArgumentDataMember = "MonthYear"
    chartNewCusts.SeriesTemplate.ValueDataMembers.AddRange(New String() {"NewCustCount"})

    Dim diagram As XYDiagram = TryCast(chartNewCusts.Diagram, XYDiagram)
    If diagram Is Nothing Then
        Return
    End If
    diagram.AxisX.QualitativeScaleComparer = New CaseInsensitiveComparer()

    Try
      CType(chartNewCusts.Diagram, XYDiagram).AxisY.Label.TextPattern = "{V:n0}"
      CType(chartNewCusts.Diagram, XYDiagram).AxisY.Label.EnableAntialiasing = DevExpress.Utils.DefaultBoolean.True
      CType(chartNewCusts.Diagram, XYDiagram).AxisX.Label.EnableAntialiasing = DevExpress.Utils.DefaultBoolean.True
    Catch ex As Exception
    End Try
End Sub

Private Function GetSales() As DataTable
    Dim table As New DataTable("Sample")

    table.Columns.Add("MonthYear", GetType(String))
    table.Columns.Add("GroupField", GetType(String))
    table.Columns.Add("NewCustCount", GetType(Integer))

    Dim row As DataRow = Nothing

    row = table.NewRow()
    row("MonthYear") = "01-2015"
    row("GroupField") = "Customer Referral"
    row("NewCustCount") = 1
    table.Rows.Add(row)

    row = table.NewRow()
    row("MonthYear") = "01-2015"
    row("GroupField") = "Walk-In"
    row("NewCustCount") = 1
    table.Rows.Add(row)

    ' ...
    Return table

End Function

AxisX axisX = ((XYDiagram)chartControl1.Diagram).AxisX;
    axisX.QualitativeScaleComparer = new ArgumentByTotalComparer(argTotalDict);
}

Dim axisX As AxisX = CType(chartControl1.Diagram, XYDiagram).AxisX
    axisX.QualitativeScaleComparer = New ArgumentByTotalComparer(argTotalDict)
End Sub