1999 infiniti i30 rear moves/sways to the right side

[Uni.wave]

I've noticed when I drive at times not all the time that the rear moves to the right side. Like it sways to that side.

Plus some dash board symbols have lit up. Such as the service engine soon, engine oil symbol, battery and brake.

Additionally, when I was driving I noticed as I looked to the rear threw the mirror I saw some smoke coming out from the muffler.

[NutriaforBreakfast]

This might be a good place to start

http://www.nicoclub.com/service-manual?fsm=I30/1999/ra

Since the I30 and Maxima are the same you might try to search for
information about the rear axle. I did not change out parts for the
rear axle but "almost" did.

[vonscorpio]

Lots of possible issues there. As NutriaforBreakfast said, the FSM is a great place look.

Here are my guesses, based on the details you provided:
Usually the brake/battery lights combo indicate your alternator has failed, or at least quit producing the correct voltage.

The oil light means please check your oil levels... now. Or yesterday would be better. It's possible that the sensor is bad, but unlikely. My I30 didn't really burn oil but until I replaced the front seal and valve cover gaskets, it did drip oil.

The sway in the backend is most likely due to one or both struts failing. Before I replaced all 4 struts, my I30 became almost un-drivable at freeway speeds due to how squirrely/bouncy it was.

Throwing random guesses at the CEL and smoke out the tailpipe, I would suspect the O2 sensor(s). Autozone will tell you the engine codes for free.

[NutriaforBreakfast]

You might go the Midas and see what they say about your
front and rear suspension components ( a free inspection). Take their
inspection and read the FSM about the components they want
to sell you and see if what they told you was reasonable.