This constant is not needed, and if you decided to rename the class to `DomainNameService`, it would be telling a lie:

>     Private Const CLASS_NAME As String = "DSN" 'for error handling

Instead, use `TypeName(Me)` to get the class' name as it appears at runtime.

The class has roughly 800 lines of code. Let's look at its public interface... side note, the inconsistently specified accessibility modifiers made me wonder what the default was in [tag:vba] (if it's not specified, it's `Public`).

So:

    Public Property Get Name() As String
    Public Property Let Name(String) As String
    
    Public Property Get Driver() As eDSN_Driver
    Public Property Let Driver(eDSN_Driver)
    
    Public Property Get DriverName() As String
    
    Public Property Get DSNType() As eSDN_type
    Public Property Let DSNType(eDSN_type)
    
    Public Property Get BitMode() As eDSN_Bitmode
    Public Property Let BitMode(eDSN_Bitmode)

    Public Property Get DriverFile() As String
    
    Public Property Get Description() As String
    Public Property Let Description(String)
 
    Public Property Get Server() As String
    Public Property Let Server(String)

These "shared properties" are the properties of *one* type. The "Oracle properties" are members of *another* type, and the "SQL properties" are members of another type. I mean, I'd put them in 3 classes.

---

Using an `Enum` for `Driver` is an excellent idea, it makes you avoid using *magic strings* or worse, *magic numbers*. It makes sense to use a `Select Case` to switch on an enum:

>     Property Get DriverName() As String
>     ' read only property
>     Select Case mDriver
>         Case DSN_DRIVER_EMPTY
>             DriverName = ""
>         Case DSN_DRIVER_SQLSERVER
>             DriverName = DSN_DRIVER_SQLSERVER_NAME
>         Case DSN_DRIVER_SQLSERVER10
>             DriverName = DSN_DRIVER_SQLSERVER10_NAME
>         Case DSN_DRIVER_SQLSERVER11
>             DriverName = DSN_DRIVER_SQLSERVER11_NAME
>         Case DSN_DRIVER_ORA11G
>             DriverName = DSN_DRIVER_ORA11G_NAME
>         End Select
>     End Property

However I'd do it like this:

    Property Get DriverName() As String

        Select Case mDriver            
            Case DSN_DRIVER_SQLSERVER
                DriverName = DSN_DRIVER_SQLSERVER_NAME
            
            Case DSN_DRIVER_SQLSERVER10
                DriverName = DSN_DRIVER_SQLSERVER10_NAME
            
            Case DSN_DRIVER_SQLSERVER11
                DriverName = DSN_DRIVER_SQLSERVER11_NAME
            
            Case DSN_DRIVER_ORA11G
                DriverName = DSN_DRIVER_ORA11G_NAME
            
            Case Else
                DriverName = vbNullString

        End Select

    End Property

The difference? Vertical breathing whitespace, an explicit default value for anything that doesn't fit a `Case` block, and `vbNullString` being used instead of `""`. It's just a little technicality, but consider this - `""` is *not* equivalent to `vbNullString`:

    ?lenb(vbnullstring), lenb("")
     0             0 
    ?strptr(vbnullstring), strptr("")
     0             56023156 

If you *really* don't like maintaining a `SELECT CASE`, you could be maintaining a `Dictionary` instead (see [this post](http://codereview.stackexchange.com/questions/45666/dictionarytkey-tvalue-implementation) for the implementation I'm referring to):

    Private DriverNames As Dictionary

    Private Sub InitializeDriverNames()

        DriverNames = New Dictionary ' this also works with a Scripting.Dictionary
        DriverNames.Add DSN_DRIVER_SQLSERVER, DSN_DRIVER_SQLSERVER_NAME
        DriverNames.Add DSN_DRIVER_SQLSERVER10, DSN_DRIVER_SQLSERVER10_NAME
        DriverNames.Add DSN_DRIVER_SQLSERVER11, DSN_DRIVER_SQLSERVER11_NAME
        DriverNames.Add DSN_DRIVER_ORA11G, DSN_DRIVER_ORA11_NAME

    End Sub

And then you can add a call to `InitializeDriverNames` in `Class_Initialize()`, and the `DriverName` getter can look like this:

    Public Property Get DriverName() As String
        Dim outResult As String
        If DriverNames.TryGetValue(mDriver, outResult) Then DriverName = outResult
        'If DriverNames.Exists(mDriver) Then DriverName = DriverNames.Item(mDriver)
    End Property

The commented-out line shows how to make it work with a `Scripting.Dictionary`.

---

I like these two:

>     Private Sub ErrRaise_NotSupported()
>         Err.Raise vbObjectError + 25010, CurrentProject.NAME & "." & CLASS_NAME, "Driver does not support the property."
>     End Sub
>     
>     Private Sub ErrRaise_DriverNotSet()
>         Err.Raise vbObjectError + 25020, CurrentProject.NAME & "." & CLASS_NAME, "Driver property is not set."
>     End Sub

However I'd write them like this:

    Private Sub RaiseNotSupportedError()
        Err.Raise vbObjectError + 25010, CurrentProject.NAME & "." & TypeName(Me), "Driver does not support the property."
    End Sub
    
    Private Sub RaiseDriverNotSetError()
        Err.Raise vbObjectError + 25020, CurrentProject.NAME & "." & TypeName(Me), "Driver property is not set."
    End Sub

And `errBox` should be called `ShowErrorBox` or similar, i.e. it should start with a verb, too.

---

Avoid comparing a `Boolean` with `True` or `False` like this:

>     If bool = True Then

`boolAsString` could be written like this:

    Private Function boolAsString(ByVal value As Boolean) As String
        boolAsString = IIf(value, "T", "F")
    End Function

`IIf` is generally frowned upon because both statements get evaluated no matter what, but in trivial string assignations like this, it doesn't matter.

...OTOH, food for thought:

    If Me.TrustedConnection = True Then
        .value = "Yes"
    Else
        .value = "No"
    End If

---

There's a lot more to say about your code, but I'd strongly recommend you extract the SQL-specifics into its own class, and do the same for the Oracle-specifics - you'll have 3 shorter, more cohesive classes.