This line causes an error:

Write tMessage.Name,!

Your class does not have Name property, so it causes an error.

The following method works :

/// Do ##class(Testing.Messages.Session).test()
ClassMethod test()
{
    Set messagedata = "<?xml version=""1.0"" encoding=""UTF-8""?><session><sessionId>124364</sessionId><cabinet>demo</cabinet><eventType>IN</eventType><eventTime>20161006160154</eventTime><login>test</login><loginFirstName>test</loginFirstName><loginLastName>test</loginLastName></session>"
    Set reader = ##class(%XML.Reader).%New()
    Set status = reader.OpenString(messagedata)
    Do reader.Rewind()

    If $$$ISERR(status) {do $System.Status.DisplayError(status)}

    // Associate a class name with the XML element name
    Do reader.CorrelateRoot("Testing.Messages.Session")

    // Read objects from xml data
    While (reader.Next(.tMessage,.status)) {
        Do:$$$ISERR(status) $System.Status.DisplayError(status)
        Write tMessage.sessionId,!
    }
}

Terminal:

USER >do ##class(Testing.Messages.Session).test()
124364

Disclaimer. I am not familiar with EDI.

Some solutions would be:

• Get official EDI 271 xsd schema files and import them into Caché
• Alternatively you can read EDI 271 specification/check examples and write your own classes

Then you need a dtl to transform incoming message into your new classes. If there's a lot of them maybe it would be better to write one generic transformer or write a transformer generator based on class (which would generate transformation method based on class properties).

After that you  can transform your class object into json via several ways:

• Old json via %ZEN.proxyObject/%ZEN.auxillary.jsonProvider
• New json via dynamic objects

The CALLIN^%ZSTART entry point gets executed when an external program begins or completes a callin. You can add logging there to see if something initiates callin.