Hesitation/Stuttering Issues

Greetings Everyone!

I’d like to share my headache with the community in hopes that someone can help. I have a 2002 jeep wrangler TJ, 4-cylinder and lately it has been stuttering/hesitating after the car reaches its’ operating temp.
To give more context, I’ve had a similar issue recently that a local mechanic said resulted from a bad o2 sensor and exhaust leaks. He fixed what he could and replaced the sensor. This fixed the issue, but he did mention there was another leak in the manifold that he couldn’t get to? I asked him if it was okay to drive for the time being and he said yes. A couple months have passed and I’m now getting the same issue. I’m wondering if it is a result of the leak and if I’ve worsened the situation? Currently I’m noticing the same hesitation/stuttering accompanied now by a strong exhaust smell while driving. Also there seems to be a buildup on the engine itself as if there is an oil leak. I’m not 100% everything is related, but I’m willing to bet they have stemmed from the same unresolved issue.

I realize this jeep is 12 years old and that things are bound to happen. Unfortunately, I’m a broke college student and I’ve already spent quite a bit on other repairs recently. (new radiator, oil pressure sending switch, power steering sensor, leak repair, etc.) I’m at my wits end because this is my daily driver and I don’t want to exacerbate the problem!

If there’s a leak in the exhaust manifold before the #1 O2 sensor, this can cause the fuel trim to be incorrect.

When the engine is cold, the computer doesn’t use the information from the O2 sensor because the engine management system is in the open loop mode. But once the engine reaches operating temperature and goes into the closed loop mode, the computer then uses the information from the O2 sensor to adjust the fuel trim.

So the exhaust leak can be causing your problem once the engine reaches operating temperature.

Tester