Q&A

 Master

P0125 indicates that the engine controller thinks that the engine is running cold, like if the thermostat was out of calibration or stuck open. Could also be a failed Engine Coolant Temperature (ECT) sensor, the engine could be running at the right temp but the controller thinks it's running at -40degreesF and setting the fuel and spark accordingly.
P1130 indicates that the controller detects an AIR/FUEL sensor (A/F = oxygen sensor, basically) heater control malfunction.
P1135 indicates an AIR/FUEL sensor range/performance malfunction.
Misfire at cruise could be caused by the engine running too cool and a failed A/F sensor would make it worse.

Most likely the P1130 and P1135 are due to a failed AIR/FUEL sensor but it could be in the wiring or connectors so it's a good idea to check the sensor and circuit to be sure you need a new sensor before you replace it. I see a list price of about $220 for the A/F sensor..
Here's a directory link for you:
http://repairpal.com/directory?address=42240&car_brand_na...