I don't think your car has an ECU. In 83 the K-cars 2.2L American engine had a spark control unit near the battery. However, the shop manual does not show a similar unit for controlling the 2.6L Japanese engine. There might be a digital computer inside the car for the MPG and range, but I can't seem to locate it quickly in the 83 service manual.
The one at Rockauto and on Ebay corresponding to P/N 5231980 is listed in the Mopar parts book as a logic module.
Try
LH front engine compartment area for a combustion controller computer used on 2.6l engines. (Chrysler Parts book lists this part shown below as P/N MD080152 as a carb emission controller for 2.6 liter.)
See locations in description in link below.
http://www.ebay.com/itm/ECU-ECM-COMPUTE ... c6&vxp=mtrMany of the early K-cars with the 2.6L engines had problems with the carburetor and/or vacuum related problems or sensor problems causing problems resulting in poor driveability and/or poor or erratic idle. In addition, the timing chain or balance shaft chain were problematic.
I suggest you buy a set of dealer factory service manuals including the wiring diagrams on Ebay. You can find a set cheap on Ebay (if you look awhile) as its an 83. (Maybe $10 for the pair of main manual or $15 for all 3.)
The electrical and engine performance volume includes wiring diagrams.
Chassis and body is the main repair volume.
There is also a supplement.
See some links below.
http://www.ebay.com/itm/1983-Dodge-Chry ... bb&vxp=mtrhttp://www.ebay.com/itm/1983-CHRYSLER-P ... 2e&vxp=mtrhttp://www.ebay.com/itm/1983-Omni-Horiz ... 71&vxp=mtrhttp://www.ebay.com/itm/1983-Chrysler-C ... 2306feaeca