I share your view that through trains via Oxford Road are unlikely, but will check the limited number of sources that I have relating to the period between the opening of the CLC Chester Line (1875) and that of Manchester Central (1880). Apart from MSJA services, the LNWR service from the South Junction Platforms at London Road/Oxford Road to Liverpool Lime Street via Lymm and Ditton Junction was the only service over this route to my recollection (prior to the closure of Central in 1969). To these may be added the limited service to Crewe via Middlewich which pre-dates my experience - but was still running in 1939.
On checking I've made an error.
The service to Crewe via Middlewich in 1922 comprised one Monday to Friday train conveying through carriage(s) between Oxford Road and Euston (though the timings suggest that the train continued in service to London Road northbound). Northbound this was attached to the 230pm 'Liverpool Express' from Euston which also conveyed through carriages to Southport and reached London Road at 712pm. The up working left Oxford Road at 1030am reaching Euston at 310pm having joined the 1105am from Liverpool which also conveyed through carriages from "Central Wales Spas and Aberystwyth". These appear to have originated at Llandovery 855am and Aberystwyth 800am; combined at Shrewsbury and with the Liverpool/Oxford Road portion at Stafford via Newport (Salop). This information from the Bradshaws for July 1922 (reprinted by D&C in 1985).
The LNWR Society had the good sense to reprint the LNWR Marshalling Circular for Summer 1910 (in 1978) and this provides more fascinating detail. At this time the down working left Euston at 2pm (there was also a connection at Crewe to Oxford Road via Middlewich off the 530pm ex Euston). The 2pm departure was the "Glasgow, Edinburgh & Aberdeen Corridor, Luncheon & Dining Car Express" and also conveyed a "Furness Line" portion. This left Euston with a four-coach portion for Glasgow behind the loco comprising a Brake Third (Brake compartment leading), a Compo. Dining Car, a Composite and a Break Third (Brake compartment trailing). Then came the three-coach Edinburgh portion led by a Compo. Dining Car, then a Composite and lastly a Brake Third (Brake compartment trailing). A Brake Composite with Brake compartment trailing comprised the Aberdeen through carriage. These eight coaches for Scotland were all down to be 65ft West Coast Joint Stock (dual-fitted) coaches. Next came a 57ft Brake Composite with a Brake Compartment at each end (have a look at the LNWR Society web-site if you haven't got a copy of Jenkinson's LNWR Carriages book to hand: Diagram 205 might be the one) for Whitehaven and, finally, our through coach (length unspecified) which was down to be a Brake Tri-Composite (with brake compartment in centre). Interestingly there is a footnote stating that when the Scotch train is too heavy (ie. has been strengthened to such an effect) then our through carriage will instead leave Euston at 206pm and be attached to the 220pm from Willesden (which conveys carriages from Bournemouth, Deal and Eastbourne to Manchester, also Eastbourne to Liverpool and Eastbourne to Birmingham - but a whole other story!) at Willesden. When this occurs our brake tri-composite will go at the head of the train (perhaps the 206pm would otherwise have been a Light Engine from Euston to take over at Willesden?) but with a 'leader' (presumably something like a parcels vehicle) between it and the loco. In either case it escapes from its companions at Crewe. An equally interesting arrangement applied to the up working.
Other trains between Northwich & Sandbach appear to be locals, often Rail Motors (Push & Pull?) with some through running to/from Acton Bridge. In the summer of 1939 there was even an 805am Summer Saturdays train from Sandbach to Blackpool North by this route.
My mistake was in saying that the through service to Oxford Road was still running in 1939. It appears to have been withdrawn in the Autumn of 1933 (see page 32 of the 1973 edition of the Oakwood book on the MSJA). This book also records an interesting service that I'd totally forgotten: From December 1st 1879 until withdrawal from March 20th 1880 there was a service from Manchester Central to London Road via Sale, Baguley and Tiviot Dale. This used the seriously long gone north to east curve south of Timperley and, if memory of another source is correct, the not quite so long gone curve from Tiviot Dale to Reddish North rather than the route through Woodley and Guide Bridge (but I could be wrong on that bit).
Also I now know that whilst Central opened in 1880 there was a temporary station there from July 9th 1877 and Chester Line services switched to it (vice Oxford Road) from July 1st 1878; the permanent station opening exactly two years later.
Finally in putting these snippets together I've consulted the April 1910 Bradshaws, a very big purchase for me from the old Sherratt & Hughes bookshop in Cross Street Manchester (did it also have an entrance in St Ann's Square or is memory failing?) in 1968 (84 shillings!). Alongside the times of the through coaches via Knutsford from Euston I noticed the other through service between Oxford Road and Euston (running in the opposite direction too) that is the one between Bolton Great Moor Street and Euston.
Anybody got a spare time machine?