PhD study (University accreditation) and the ability to teach in the USA
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.