Spanish speakers: What is the difference between idioma, dialecto, lengua and lenguaje?

I hear mexican people say that Ingles es una otra idioma, pero refieren a Nahuatl como lengua.Spanish speakers: What is the difference between idioma, dialecto, lengua and lenguaje?
Idioma: Language spoken by a community.
Lengua: Linguistic system characterized by being fully defined, by having a high level of nivelation, by being vehicle of a differentiated culture and, on some occasions, by having imposed to other linguistic systems.
Lenguaje: A group of articulated sounds through which people convey what they think or feel.
Dialecto: Variety of a same language adopted in a concrete geographical zone.