MPs can be on 4 MEA-linked bodies without being disqualified:

MPs who are members of four bodies functioning under the Ministry of External Affairs would continue to remain out of the ambit of 'office of profit' law and would not attract disqualification, a Parliamentary panel has said.
The Joint Committee on Office of Profit in its latest report has recommended that The Indian Council for Cultural Relations, Research and Information System and Hindi Salahakar Samiti of the External Affairs Ministry should remain listed under the relevant sections of the Parliament (Prevention of Disqualification) Act, 1959, the membership of which should not disqualify a Member of Parliament.
The Committee, headed by Satyapal Singh (BJP) also said it agrees with the view of the MEA that membership of the Indian Council of World Affairs should not be considered 'office of profit' and therefore not be listed specifically in the schedule of the disqualification law.

Referring to the Haj Committee, the panel felt that it exercises various executive functions which makes it an 'office of profit' entailing disqualification of a member.
It said Haj Committee should remain on the schedule of the disqualification law to ensure MPs are not disqualified for being its members.
Except for Research and Information System, MPs are members of all the bodies under MEA. There is a provision for an MP to be nominated to Research and Information System but apparently no one has been nominated to it.