There are no more Delta routes in WV. The political history is that there was a big federal government take everybody to jail event in the 1960s at the then called State Road Department. In WV there are a lot of roads that just developed. Coal company built it, early settlers built it, railroad built it, whatever. People live there, somebody has to keep it up and, as noted, WV has no real county highway departments, "County" (the circle signed routes) is just a lesser quality (generally) state highway. So, the state was in the practice of fixing all of these back roads, but there was no accounting. A "road" a crew "fixed" might be some pol's driveway, or might just be "we took the gravel and sold it and split the cash". Since there was no way to account, there was no way to check. So, as a result of the investigation, they came up with the "Delta" route, which were roads to which the state made no right of way claim but which none-the-less repaired by the state. All road work has to be "charged off" to a route number and a mileage. So, if you say you did X to Delta 78, 3 miles from the JCT of CR 6/89, then an inspector can go look at it and there better be X there. However, this was just a short term way to get the corruption under control. By the mid 70s all Delta routes were either established right of way in the state and became County routes, or were abandoned and no longer are under state maintainance. Any Delta signage you see today is just old signage that never got taken down.
As to the "pentagon", this is not the standard county route pentagon sign used in most states, which has equal sides and rounded corners. Its supposed to be a picture of a little house (think monopoly houses) with unequal sides and sharp corners. The program was under a single term governor, Underwood. The program was called "HARP", for Home Access Roads Program. It was all politics. People up a holler, or in a subdivision, filled out a petition and got a sign and "maintain at the current standard" status. There was no right of way check. The next gov cancelled it on day one. But the state is stuck with all of these HARPs, which it has to keep up. Technically, they are County routes, you would account for work on one as "County HARP 456" for example.