Whether one should move to CAT or Hon'ble High court?

For challanging the recruitment/advirtisement  a writ under Article 226 lies before the High Court not before the CAT

Matters after joining the employment should approach the CAT if covered under CAT.

If you are not satisfied by the order of CAT then file a writ before High Court under Article 226 which will be heard by Division Bench.

Now Central Govt have directed to file

 I am sorry to differ with Tribhuwan C Pandey. 

1. Pl. refer to preamble to Administrative Tribunal's Act. It has jurisdiction to try all matters relating to service including recruitment into service, appointment etc.

2. The section referred to, that appeal lies to Supreme Court has been set aside by Supreme Court in the case of L.Chandra Kumar. 

3. Consequent upon the judgement, an appeal lies against the judgement of CAT before High Court, in the form of a Writ petition which is to be heard by a Division Bench.

correct. recrument matters  so far govt service is concerned can be challenged in tribunal. i have seen tribunal state heard irregularities  in recrument , names coming through employment exchange, similar matters more than 100 cases a day.against order of tribunal you can challenge before high court in writ jurisdiction.high court is the scrutiny authority ie- bit lesser than review.i have gone through the original order of supreme court  regarding this. but in reallity high court act like an applate court

You questions are answered as under :-

Whether CAT like has the power to quash down the irregularities if found in an organization over the recruitment?

Ans : Yes

As per the Administrative tribunal act -1985, the appeal only lies to the  Hon'ble Supreme Court of India,whether aggrieved party can move to the Hon'ble High court under Article 226/227 of constitution of India?

Ans : High Court

Whether doctrine of  res judicata will operate?

Ans : What do you mean by res-judicata in undecided issue?