Referencias: 
1) https://stackoverflow.com/questions/3516119/get-post-to-restful-web-service
2) https://stackoverflow.com/questions/11388714/how-do-i-use-msxml2-serverxmlhttp-to-grab-data-from-another-site

Script de Ejemplo para enviar un SQL:
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Dim sUrl As String
Dim variablesPost As String
Dim response As String
Dim xmlhttp

Set sUrl = "http://tecno.sistemasiad.com.ar/public/api/SQL/111/A/CLASEXTECNO"

Set xmlhttp = Server.CreateObject("MSXML2.ServerXMLHTTP")
xmlhttp.open "POST", sURL, False
xmlhttp.setRequestHeader "Content-Type", "application/x-www-form-urlencoded"

variablesPost = "sql=Insert into clientes (...) values (...)"

xmlhttp.Send variablesPost

xmlhttp.send()

Dim response As String = xmlhttp.responseText
Response.Write xmlhttp.responseText

Set xmlhttp = Nothing



Script de Ejemplo para enviar un ABM de Cliente:
------------------

Dim sUrl As String
Dim response As String
Dim xmlhttp

Set sUrl = "http://tecno.sistemasiad.com.ar/public/api/BATCH/CLIENTE/111/A/CLASEXTECNO"

Set xmlhttp = Server.CreateObject("MSXML2.ServerXMLHTTP")
xmlhttp.open "POST", sURL, False
xmlhttp.setRequestHeader "Content-Type", "application/x-www-form-urlencoded"

variablesPost = "id_externo=12345"
variablesPost = variablesPost & "&nombre=Julia Maria"
variablesPost = variablesPost & "&apellido=Perez"
variablesPost = variablesPost & "&tipo_de_documento_id=......."
variablesPost = variablesPost & "&nro_de_documento=......."
variablesPost = variablesPost & "&domicilio=......."
variablesPost = variablesPost & "&localidad_id=......."
variablesPost = variablesPost & "&situacion_de_iva_id=......."
variablesPost = variablesPost & "&telefono_fijo=......."
variablesPost = variablesPost & "&telefono_celular=......."
variablesPost = variablesPost & "&email_correo=......."
variablesPost = variablesPost & "&observaciones=......."
variablesPost = variablesPost & "&created_at=......."
variablesPost = variablesPost & "&updated_at=......."
variablesPost = variablesPost & "&user_id=......."
variablesPost = variablesPost & "&zona_local_id=......."
variablesPost = variablesPost & "&sucursal_id=......."
variablesPost = variablesPost & "&id_de_importacion=......."
variablesPost = variablesPost & "&fecha_de_baja=......."

xmlhttp.Send variablesPost

xmlhttp.send()

Dim response As String = xmlhttp.responseText
Response.Write xmlhttp.responseText

Set xmlhttp = Nothing