As has been said, the Stafford to Wellington line closed whilst still steam operated, possibly from the Stafford end. There is a video on You Tube of a complete trip towards the end, and showing the various loco types encountered en route.
Shrewsbury to Wolverhampton was affected by a couple of key events, as well as the usual modernisation and Beeching issues - these are transfer of the WR route to the LMR in 1963 and full introduction of the WCML electrification through Birmingham, Wolverhampton, Bescot and to Walsall in March 1967.
For actual locos, Paddington to Birkenhead was dieselised with Western class diesels after the Kings allocated to Stafford Road were withdrawn - 1962. Any OOC allocated ones built up to late 63/early 64 were used - my limited personal experience included the low numbered ones (eg D1011). These were replaced by either brand new or almost new Brush Type 4s from 1964 - D1682-D1690, D1695/6 and various in the low D17xx (except 1702-6 - later ER class 48s), allocated to Oxley but OOC and other ones appeared - say up to D1757 - NB the several months old D1734 (Bristol Bath Road) came to grief adjacent to Coton Hill yard when it struck wagons derailed in the yard which fouled the main line - one of the D168x which was nearby in the yard was damaged also. D1734 was the shortest lived class 47 of all. Note there was still a lot of steam on freight on the ex WR Midland area lines in the mid 60s. Stanlow to Albion block oil trains were also run by Birkenhead 9Fs until the mid 60s when replaced by class 47s.
DMUs from the usual Tyseley pool of class 116 (50050-79/85; and a handful of the ex Cardiff and Bristol ones) would have appeared along with class 122 (55002-10; also 12 and 13 at times, though odd ones of these seem to have been swapped to and fro with Laira) - after closure of Much Wenlock and the Severn Valley north of Bewdley, other than as additional power cars or replacement power cars in class 116, there doesn't appear to be any reason for these to have appeared. Class 128, 55992-55996 may also have appeared. All of these went from W to M prefix in 1963. Some 116 and 122 were still in that almost malachite green colour.
Class 40 were prevalent in the Birmingham area (of the WMCL allocated batches - 210-236, 255, 267-9, 287-344, 369-384 or thereabouts - so all three headcode or not variants).
From March 1967, with full electrification of the WMCL routes through services from Wolverhampton Low Level to Birkenhead ceased - passenger trains generally terminated terminated at Wolv High Level - a batch of 3 car class 119 and 101 (the latter being the last 5 sets from the Lichfield - Birmingham line batch 50316-50320) were allocated to Chester for these services - they were all repainted (the 8 X 119s in blue/grey - 51085-87; 51099-51104 etc).
Any Stoke or Birmingham Division class 24/25 may have appeared on freight/parcels but probably more likely after early 1967. Livery celebrities like D5021 and D5028, and some of the final batch eg D7670 and D7677 were regular performers on freight from Bescot. D5000-49, and 73-93 were Stoke Division from 1967/8. 5000 was stored after withdrawal at Shrewsbury. The local 47s and 24/25s are likely to have run any freight in the remaining bits of the Stafford line.
Until the later 60s, locos tended to remain in their allocated areas - however as the era wore on so the appearance of, for instance, ER class 47 became more regular, say at Bescot.
Hope this helps you.