Air carrier pilot reported they navigated to fix OYVEY when their instruction was direct ELVAY due to very similar sounding fix names.

Narrative

On climb out; while executing the EWR departure from 22R; the Departure Controller issued us instructions to turn direct to ELVAY intersection. We heard and read back intersection OYVEY; a fix further down our flight plan route. We then proceeded direct to OYVEY. Shortly after; we were instructed to switch to the next NY frequency. After checking on; this Controller queried us on our course; which we replied we were direct OYVEY. She clarified we were supposed to proceed direct ELVAY and gave us a heading. From there she cleared us direct to another fix on our original route and the flight proceeded uneventfully. While the two fixes look very different on paper; when said aloud and extremely fast as is typical in NY airspace; they sound very similar. The EWR departure off 22R; on this type aircraft; is required to be hand flown. It has several early turns and a level off at 2500 ft. resulting in a high workload. Very busy; very congested airspace with radio calls coming extremely fast.The two fixes sound very similar over the radio; restricting direct clearance to OYVEY on departure when ELVAY is being used. I need to pay closer attention to the first couple fixes on departure and how they relate to each other while briefing at the gate; so I can identify possible fixes that could be confused under high workload. Controllers talking too fast over the frequency has always been a problem in NY airspace. I understand the high workload they operate under; but rushing clearances will only result in misunderstandings; especially when we are under a high workload on departure.