For Rishton-Warrington, the only permitted route is Rishton-Preston-Warrington, with Preston-Warrington only allowed via the West Coast Mainline: see Routeing Guide map KW
For Warrington-Banbury, you can either trace a non-doubling-back route on Map RM (Warrington-Crewe-various routes-Birmingham-Banbury) or on a combination of Maps NR + RM (Warrington-Manchester-Wilmslow/Cheadle Hulme on Map NR, then Wilmslow-Crewe-various routes-Birmingham-Banbury or Cheadle Hulme-Stoke on Trent-various routes-Birmingham-Banbury on Map RM)