It sounds like a CV joint is going bad. Check under the front of the vehicle for a torn CV joint boot. Often times these tear and allow dirt into the joint making them go bad.
The 2013 Jeep Grand-Cherokee's turning circle is 37.1 ft..
The 2004 Jeep Grand-Cherokee's turning circle is 37.4 ft..
I had that same exact problem with a 1995 Jeep Cherokee, and it was indeed a bad oxygen sensor. Relatively cheap repair too.
Usually a bad turn signal flasher
Viscuous coupling in the transfer case could be going bad.
Bad flasher?
The 2011 Jeep Grand-Cherokee's turning circle is 37.1 ft..
The 2005 Jeep Grand-Cherokee's turning circle is 36.7 ft..
The 2012 Jeep Grand-Cherokee's turning circle is 37.1 ft..
The 2004 Jeep Grand-Cherokee's turning circle is 37.4 ft..
The 2007 Jeep Grand-Cherokee's turning circle is 36.7 ft..
The 2009 Jeep Grand-Cherokee's turning circle is 36.7 ft..
The 2003 Jeep Grand-Cherokee's turning circle is 37.4 ft..
The 2001 Jeep Grand-Cherokee's turning circle is 37.4 ft..
The 2010 Jeep Grand-Cherokee's turning circle is 37.1 ft..
The 2014 Jeep Grand-Cherokee's turning circle is 37.1 ft..
The 2013 Jeep Grand-Cherokee's turning circle is 37.1 ft..