CRJ-700 Captain reported a fumes event after pushback/engine start and returned to the gate.

Narrative

After pushback from ZZZ gate XX; engine start and APU shutdown I was immediately hit with a very strong smell of fumes from the air conditioning vents. I confirmed with the First Officer that he smelled it as well. I called the Flight Attendants (FA) to ask if they noticed anything; and the aft FA reported the same condition - a very strong smell of fumes. The aft FA described it as a 'burning oil' smell. The forward FA said that he had not yet smelled anything; but cautioned me that he has a very weak sense of smell. I looked through the QRH and found the Smoke/Fire/Fumes procedure. This procedure did not specify In Flight/On Ground; and the procedure seemed to be written towards being in flight. The procedure was very involved and attempted isolation of a specific bleed source/pack. Because we were on the ground and pressurization/bleed air was not needed; I elected to close the bleed air valves entirely to stop further fumes from entering the cockpit and cabin. I did not want to subject myself; the other crew members and passengers to further fumes in attempt to isolate the issue to a specific bleed source or pack; when bleed air was not needed for safety of flight. Once the bleed air valves were closed; the fumes began to dissipate. During this time I communicated with our Dispatcher and Maintenance Control; who directed a gate return. As we returned to the gate; I began to experience a headache; my eyes were watery and heavy; and I recognized that I was having a reaction to the fume event. Other members of the crew also reported effects from the fume event; including headache. I was ultimately removed from duty and treated by medical professionals. When we returned to the gate; the forward FA told me that he began noticing the fumes; as did the (Customer Service Agent) who met us for the gate return.Fumes were introduced into the cockpit and cabin by the packs after engine start and APU shutdownI understand that ZZZ maintenance ran the engines and could not duplicate this fume event. The aircraft was then placed back into service. I wish that maintenance would be required to investigate the event further; to hopefully prevent it from happening again. I suspect that one of the engine oil seals is leaking which caused oil to puddle at an inappropriate location inside the engine. The aircraft had been parked for approximately 19 hours; which would have allowed a lot of time for oil to leak through a bad seal inside the 'cold' engine and puddle. When we started the engines and shut down the APU; the engine bleeds opened to the packs which I believe pushed the oil (which had now been heated inside the engine) into the pack system. I believe that maintenance was unable to duplicate this event because the engines had now been operated previously; which cleared the oil that had accumulated over the 19 hours that the aircraft was parked. It is my opinion and suggestion that maintenance should be required; without exception; to investigate an issue of this severity further than just running the engines and placing the aircraft back in service.