When you set the AutoSizeDropDownToBestFit property to true, the column's width will be sized according to its content. The code snippet below demonstrates how can achieve it: 
void radGridView1_CellEditorInitialized(object sender, GridViewCellEventArgs e)
{ 
    var editor = e.ActiveEditor as RadMultiColumnComboBoxElement;
    if (editor != null)
    {
        editor.AutoSizeDropDownToBestFit = true;
    }
}

Another way is changing the MultiColumnPopupForm`s size: 
void radGridView1_CellEditorInitialized(object sender, GridViewCellEventArgs e)
{
    var editor = e.ActiveEditor as RadMultiColumnComboBoxElement;
    if (editor != null)
    {
        editor.PopupOpening -= editor_PopupOpening;
        editor.PopupOpening += editor_PopupOpening;
    }
}

void editor_PopupOpening(object sender, CancelEventArgs e)
{
    if (sender is RadMultiColumnComboBoxElement)
    {
        RadMultiColumnComboBoxElement el = sender as RadMultiColumnComboBoxElement;
        el.MultiColumnPopupForm.Size = new Size(350, 150);
    }
}