Oval chainrings have come and gone multiple times over many decades. I have yet to see any convincing evidence that they provide a real advantage, but some riders swear by them. My girlfriend's new hardtail has one and she says she can feel a difference, but whether that translates into a performance improvement is impossible to tell.
One thing you may run into is shifting issues if you run a 2x setup, since the outer chainring is only close enough to the front derailleur to shift properly at two points per revolution. There could be a slight increase in chain drag if you run a rear derailleur with a clutch, since the cage moves back and forth constantly, but off-road, there's not likely to be a significant difference, since the chain is bouncing most of the time anyway.
If you need to replace your chainring(s) anyway, perhaps it's worth a shot, but I wouldn't spend extra money just to try them. That's probably just the frugal Yankee in me.
I used elliptical chainrings on my road bike for several years. I currently have an elliptical chainring on my MTB (single chainring).
There have been a number of studies. Some conclude that it does improve performance. Some conclude that your body adapts, so there is no difference. Some of the Team Sky riders use non round rings, including TDF winners, so there is that.
My own personal experience is that they do help on climbs, on both dirt and pavement, but hurts on downhills, when on the road, because you can't spin as fast. Off road, I'm usually not pedaling that fast on downhills, so it isn't an issue.
When I had them on my road bike, with double chainrings, it took some fiddling around to get the shifting right, but had no problems after that. On an MTB with single chainring, there is no issue with shifting at all.
My advice would be to get one if you have an MTB with single chainring. If you are wealthy, you might try them on your road bike. You might like them, you might not. I've been thinking about getting a set for my current road bike, but don't want to spend the money.
Like Rock Creek Rider said, there have been studies that show that riding an elliptical does have benefits. For direct evidence, if you look at how Rotor cranks show data, they can even give you an optimized chainring angle so that you have a smaller "dead spot" in your pedal stroke. That is, you install the Rotor ring with power meter, do a training session, and the software calculates a personalized recommended adjustment based on where the power meter notices that you are and are not generating power in your pedal stroke. If your body adjusts to your new adjustment, the optimum angle may re-adjust until you get it dialed in.
That being said, to answer whether or not it's worth it: That's entirely up to you and depends on your riding style and budget. (A brand new Rotor QRing can cost about 150 USD, so it is not unattainable.) For me, it felt absolutely necessary for long distance solo rides (e.g., touring, triathlon, TTs, and training rides). Throughout the week I switch between a round ring (commuter bike) and an elliptical (training and race bikes). With my race bike, which has a Rotor 53T QRing and 2INPower, it feels like I'm generating power throughout the entire pedal stroke, and the data seems to reflect this via more consistent power readings. On the feel side, it's the same smoothness even with my old Shimano BioPace on my bad weather training bike. After riding my race bike and switching to my commuter, which has a round Shimano ring, the dead spots of a round ring then feel much more pronounced. In short, I notice a real difference between round and elliptical and prefer elliptical by miles. It's an essential piece of gear for me.