PhD study (University accreditation) and the ability to teach in the USA I'm thinking of starting doctoral studies at York University (USA). I found this on the York University website information about accreditation:


  YORK UNIVERSITY IS NOT ACCREDITED BY AN ACCREDITING AGENCY RECOGNIZED BY THE UNITED STATES SECRETARY OF EDUCATION


After finishing this doctorate at York University in the USA, could I work as a lecturer at the University or at others in the USA?

What is the general difference in the Universities accredited by the United States Secretary of Education, and those which are not?
Accreditation is supposed to enforce standards of quality in higher education institutions. If an institution does not have accreditation, then it is extremely suspect, and any degree you obtain from it is likely to be completely worthless. This is from the Wikipedia page on unaccredited institutions:


  All fraudulent diploma mills are also unaccredited schools, although they may claim accreditation from an unrecognized agency. Accreditation from such organizations, known derisively as accreditation mills, is unrecognized by any government or reputable private entity, and any courses taken or degrees received from such a school are generally considered invalid.


As you noted, the "university" claims to be accredited by the "International Accreditation Organization". This has the hallmarks of an accreditation mill as described in above.

I would be extremely wary of this particular institution, and it is unlikely that any other academic institution would hire you on the basis of a degree from it.