T137 is the Dodge truck ("T" means "truck") engineering code for the original Power-Wagon 1 ton 4X4 truck. Think of it as identifying the basic 4X4 chassis, not the body style. It is not an "engine" code and has nothing to do with engine displacement. T137 appears as the prefix on original PW engines because those engines were built (and marked) for installation in the Power-Wagon. T137 appears to have been used up to the end of domestic production in 1968 (and maybe beyond for export production), but I've never personally confirmed that late use.
T137 applied to all the different PW based model numbers, from the 1945-47 WDX to the 1948-56 PW models, through the 1958 W300M to the 1959 and later WM300. It also applies to the 1951 C78A900 Gerstenslager PW based ambulance, the 1958 and later M601 and M601A1 open cab MDAP trucks, and the 1963 M615 ambulance with the Mark Body. It most likely was used through the end of domestic PW production in 1968 to identify the chassis, even though engines MAY (I don't know) have used a different code by that time.
Dodge began using the "T" series truck engineering codes in the 1930's. The 1934 K-39-X-4 had engineering code T-9. I don't know when Dodge stopped using this "T" format of engineering code.
T137 is listed as the engineering code from 1946 through 1957. The 1958 parts manual was issued in November of 1957 and actually covers all models for both years 1957 and 1958. The model code for our Power-Wagon for 1957 was K6-W300, and it still carried the T137 engineering code. For this new year, the model code changed to L6-W300M, and the engineering code changed to L6-WM3.
1959 lists the model code as M6-W300M, and the engineering code as M6-W3M (notice how the two digits: "M" and "3" have traded places).
1960 lists the model code as P6-W300M, and the engineering code as P6-WM3 (digits are now back to their 1958 order).
1961 and 1962 both list the model code as R6-W300M, and the engineering code as R6-WM3.
There are no engineering codes listed in either the 1963 or the 1963-1968 parts manuals.
Now for the twist: The 1959 Chryco (Canada) parts manual lists for the "M" series: Dodge Power-Wagon model code M6-W300M and Fargo Power-Wagon model code FM6-W300M, both with the T137 engineering code.