Any idea what is causing this noise?
 

I've replaced the driver's side rear wheel bearing, all the CV joints, shocks, checked rear brakes, and made sure the tires are not rubbing. The noise originally started only going around right hand curves...now it's present when accelerating on the straight. When I release the gas pedal, the noise goes away.

https://www.youtube.com/watch?v=ok7jtmDvmF4&feature=youtu.be&list=UU6qMnjL Ap6r82CXJrtoHhmg

I recorded this video with my phone being held behind the driver's seat.

I can't tell which noise you're talking about. Is it the one that sounds like muffler grumble or the whining noise? If it's the whining noise, It's likely a tire rub on the fender lip. Are your tires and wheels stock size? If so and the tires show some wear spots on the outer periphery, you might check for a broken transaxle mount or loose torsion bar mounting and adjusting hardware. Is the back of the car squatting?

If it's the grumbling sound, I couldn't be helpful.

Could be trans/differential related with a bearing loading up on throttle.

The rubbing noise is my concern. I'm starting to believe the the noise is caused by a vibration. Tires are not rubbing on anything....that was my first thought. No rub marks on the tires and I have actually sprayed marking paint on the inside on wheel wells to confirm.

I pulled the transaxle mount and brace to check it and I urethaned while it was out. The car does squat when I accelerate, the noise starts when I release the clutch pedal and stops when depress the pedal. I'll check the torsion bar mounting bolts.

It may be coming from the transaxle. Is there anyway confirm without replacing or tearing apart the transaxle?

Go to shop with a hub dyno. What's your location?

I'm location in Maryland, about 30 minutes north of Baltimore.

Google returns:

Dynapack Information | JE Import Performance

I might phone and talk to them about their service and explain you're trouble shooting a drive-train noise. This would allow you to isolate the noise with and without load in a safe environment.

Great idea, thanks! I'm going to give them a call and set up an appt.

I have put the car on stands and I couldn't replicate the noise. Hopefully the hub dyno will help find the issue or at least eliminate some possibilities.

I crawled under my car this morning to check things out again. I found the front exhaust hanger is broken off and the rubber mount is missing. I made some adjustments to the muffler hanger and took the car for a test drive. I only heard the noise a couple times!! I'm crossing my fingers that the new hanger and rubber mount will fix the issue completely.

Ah, well thats an easy fix.