I'll give a shot at clearing some things up.
Delorme is wrong in a couple of places.
State Road 131 no longer exists. It was turned over to the town of Clarksville, and is now known as Lewis and Clark Parkway. It runs east/west from I-65 to the western edge of Clarksville, where it intersects with Browns Station Way.
Once upon a time US 31 split at Sellersburg, Indiana (9 miles north of the Ohio River) and 31-E ran south from Sellersburg, parallel to the railroad tracks, to Clarksville, and continued south on a route that is now covered by I-65. Two access roads on either side of I-65 are named Old Highway 31. I am not certain what path 31-E followed from Eastern Boulevard to the Ohio. I'll look that up and post it later.
As it is now, US 31 and I-65 run the same route from Eastern Boulevard for a couple of miles, then US 31 splits off again and crosses the George Rogers Clark Memorial Bridge into Louisville. I'm not sure of the exact route, but it does head out to Bardstown Road, and points south.
Back up in Sellersburg... US 31-W used to follow Indiana State Road 311 south into New Albany. In Floyd County SR 311 is also know as Charlestown Road. When US 31 was abandoned as a federal highway Indiana renamed it SR 331. It stayed that way for a few months, then was renamed SR 311. I think it may just have been a typo or a sign-maker's mistake that made it 331 instead of the current 311.
Once SR 311 (old US 31-W) got into New Albany, it followed Charlestown Road to Vincennes Street, the south on Vincennes Street to the K&I Railroad bridge, and across it into the western end of Louisville. From there it went on down to Dixie Highway, then followed (and still does) Dixie Highway to points south - I've not explored that farther.
The K&I Railroad bridge had lanes on each side of it for automobile/light truck traffic. For a time it was a toll bridge. It was closed to car/truck traffic when some fool tried to take his dump truck across it, and the railroad elected to shut it down.
US 31-W northbound heads on up toward the Ohio River, then follows Main and Market Streets (They're both one-way) to the east, where 31-W joins with 31-E and becomes whole again - US 31.
Just now, looking at google maps, it appears that the Kentuckians did everything possible to keep US 31-E & US 31-W from joining, and they for-sure didn't want to rename one or the other.
An interesting bit I found on wikipedia:
The American Association of State Highway Officials (AASHO) adopted a resolution against split routes in 1934. In order to eliminate the US 31E/US 31W split, it commissioned a new U.S. Route 37, replacing US 31E from the Louisville area south to Glasgow, and then following Kentucky Route 63 and several routes in Tennessee to Chattanooga. The rest of US 31E, from Glasgow to Nashville, was assigned U.S. Route 143; this proposed route was extended southwest to Centerville in 1938 and Jackson in 1944 via State Route 100 and State Route 20. US 31W would have become the main route of US 31. Kentucky and Tennessee refused to accept the renumbering, and never changed signs, leading AASHO to re-recognize the split in 1952.
That place in the picture where the road to nowhere is? That is an old railroad right of way. It goes west into New Albany, and northeast towards Charlestown. It was easier for Indiana, the federal government, and the railroad to just build a bridge over it than to go thru all the hoopla and red tape to get the ROW abandoned. In a rare show of intelligence, all involved decided to just skip over the problem.