Try
Dim page As XElement = <response><results><result><status>OK</status><number>phonenumberhere</number><wless>y</wless><carrier_name>ATT Mobility</carrier_name><sms_address>phonenumberhere@txt.att.net</sms_address><mms_address>phonenumberhere@mms.att.net</mms_address></result></results></response>
Me.addr = page.Element("results") _
.Element("result") _
.Element("sms_address").Value
The element you were looking for is not at the top, so page.Element("sms_address") won't find it.
Alternatively, since you're lucky enough to be using VB.NET, you can use
page...<sms_address>.Value
or
page.<results>.<result>.<sms_address>.Value