Check engin light on. There are four error codes P0137,P0141,P0342, and P1792. How do I fix it. Will I pass inspection with these codes?

Some errors will come right back. Some may stay out for a while. I knew someone that got his check engine light cleared right before testing. It would come back about a week later. Don't know what it was.

replace the 0 2 sensor
inspect the plug connection for corrosion oil or water

http://www.obd-codes.com/p0141

Definition of check engine code P1792:
Acura
TRANS EEPROM Checksum Error
Chrysler/Dodge/Jeep
Battery power was disconnected since last power down
Citroen/Peugeot
Barometer Pressure Circuit Malfunction
Ford
Barometer Pressure Circuit Malfunction
GM
Transmission Control Module Reprogrammable Memory
Honda
Problem in Engine Coolant Temperature (ECT) Sensor Circuit
Isuzu
Trans EEPROM Checksum Error
Jaguar
Ignition Supply Malfunction
Kia
Ignition Supply Malfunction
Mercedes
Barometer Pressure Circuit
Opel
CAN data bus,ECMITCM communication - malfunction detected
Volkswagen/Audi
Transmission Range Display Circ. Short to B +
Volvo
Transmission Range Display Circ. Short to B +

will code p0141 keep truck from starting

You have to realize that vehicle is15 years old and probably worth peanuts. if you repair it then a few weeks later it breaks down again you have probably wasted your money. i feel to repair it you will pay close to a thousand dollars then you don't know if it will pass a safety next year
I would scrap it and get a good one. Just to go to a dealer for a check up will cost over a hundred dollars.

P0442 FORD - Evaporative Emission System Leak Detected Small Leak

Possible causes- Missing or loose fuel cap
- Incorrect fuel filler cap used
- Fuel filler cap remains open or fails to close
- Foreign matter caught in fuel filler cap
- EVAP canister or fuel tank leaks
- EVAP system hose leaking
- Fuel tank leaking
P0136 - O2 Sensor Circuit Malfunction Bank 1 Sensor 2
Possible causes- Rear Heated Oxygen Sensor Bank 1 harness is open or shorted
- Rear Heated Oxygen Sensor Bank 1 circuit poor electrical connection
- Faulty Rear Heated Oxygen Sensor Bank 1
- Inappropriate fuel pressure
- Faulty fuel injectors
- Intake air leaks may be faulty
- Exhaust gas leaks

P0141 FORD - O2 Heater Circuit Bank 1 Sensor 2

Possible causes- Faulty Heated Oxygen Sensor (H2OS) Bank 1 Sensor 2
- Heated Oxygen Sensor (H2OS) Bank 1 Sensor 2 circuit fuse
- Heated Oxygen Sensor (H2OS) Bank 1 Sensor 2 circuit open shorted to ground
- Heated Oxygen Sensor (H2OS) Bank 1 Sensor 2 circuit poor electrical connection
- Faulty Engine Control Module (ECM)

its a rear o2 sensor code

p0325 = bank 1 sensor 2 oxygen sensor p0141 = knock sensor
if it were me you could watch the sensor on a scanner to see if working properly but without a scanner i'd replace the oxygen sensor bank 1 = passenger side
sensor 2 is sensor behind the catalictic converter screwed in

good luck

code p0342 is referring to the cam shaft. i am not getting anything for the other code for your vehicle so i would start there.