How are Victor airways defined and numbered?
The general rules for this are in FAA Joint Order 7400.2K, Procedures for Handling Airspace Matters. Chapter 20 describes when and how air routes are defined and designated, although it doesn't go into much detail about some things.

For example, the instructions on when to create a route are fairly general:


  20-1-3. WHEN TO DESIGNATE AIR NAVIGATION ROUTES
  
  ATS routes should be designated to serve en route operations when:
  
  a. The route is predicated upon NAVAIDs that are suitable for
  inclusion in the system.
  
  b. The benefits of the designation should outweigh any adverse effects
  to other airspace users, and:
  
  1. The route is a normal extension of an existing airway; or
  
  2. Users will benefit from charted information pertaining to navigational guidance, minimum en route altitudes, and changeover
  points.


Similarly, although there are some clear rules for NAVAID spacing, it doesn't tell you why a route would follow certain ones and not others:


  20-3-1. NAVAID SPACING
  
  a. VOR Federal airways are based on NAVAIDs which normally are spaced
  no farther apart than 80 NM. They may be based on more widely spaced
  NAVAIDs if a usable signal can be provided and frequency protection
  afforded for the distance required (see Order 9840.1, U.S. National
  Aviation Handbook for the VOR/DME/TACAN Systems).


The naming convention is in 20-1-5:


  20-1-5. ROUTE IDENTIFICATION
  
  Dual designation of ATS routes must be avoided. All alpha-numeric ATS
  route identifications must be assigned by Airspace Regulations and ATC
  Procedures Group as follows:
  
  a. Identify ATS routes based on L/MF NAVAIDs by color names (e.g.
  Amber, Blue, Green, and Red) followed by a number designation.
  
  1. Designate those routes extending east and west as Green or Red.
  
  2.  Designate those extending north and south as Amber or Blue.
  
  b. Identify ATS routes based on VOR NAVAIDs as follows:
  
  1. Route lettering must be as follows:
  
  (a) The letter “V" will prefix low altitude ATS routes below FL 180.
  
  (b) The letter “J" will prefix high altitude ATS routes at FL 180
  through FL 450.
  
  2. Route numbering must be as follows:
  
  (a) Assign even numbers for those ATS routes extending east and west.
  
  (b) Assign odd numbers for those ATS routes extending north and south.
  
  c. Identify advanced RNAV ATS routes as follows:
  
  1. The letter “T" will prefix low altitude RNAV ATS routes below FL 180, and the letter “Q" for RNAV routes FL 180 and above.
  
  2. Route numbering must follow the guidelines detailed in paragraph 20-1-5.b.1.(a) and b.2.
  
  d. Route segments must be listed from West to East for even numbered
  ATS routes, or South to North for odd numbered routes.


Many airways don't follow that numbering convention exactly, at least on certain segments. For example, V67 is more or less east-west between the GHM and SYI NAVAIDs although overall it's mostly north-south (from ENL to GQO). I assume that as the number of routes increased, they became longer and less consistent, possibly to avoid creating too many total routes: it looks like the lower-numbered routes are often more 'correct' than higher-numbered ones.

But just like with a road, even if it's clear why the road exists (I can see that people want to drive from A to B) it may not be clear why it follows the exact route it does (why does the road go north of that hill and not south of it?). All those 'small' decisions were made by the person who designed the route and there's probably no way to know them all.