Nketiah scored a hat-trick to continue his fine goalscoring start to the season, but it was Hudson-Odoi who was the real star at Stadium MK.
The 18-year-old was making his first competitive start for the Young Lions and it will surely be his last as he scored two scintillating first-half goals.
Chelsea's Hudson-Odoi was involved with Aidy Boothroyd's side as part of his rehab following an Achilles injury, but it was clear he was a step above this level and seems certain to be back with the senior squad for next month's Euro 2020 qualifiers.
Arsenal striker Nketiah, on loan at Leeds, also bagged a first-half brace and completed his treble after the break to take his tally to 10 in 13 games for club and country as he continues to make a name for himself – even if he did miss a late penalty.
The foundations of the win were laid with a brilliant opening 45 minutes – a barrage of pace, physicality and intent – and the three points were enough to send England top of Group 3.
Austria, who won their first three games, did deny their hosts a clean sheet after break as Christoph Baumgartner headed home, but there was no way back for them.
Boothroyd had called for his side to be more dynamic in their approach before the game and it took only 12 minutes to pay dividends as they surged into the lead.
Lloyd Kelly pinged an inch-perfect cross-field ball to Max Aarons who attacked the space down the right and centred for Hudson-Odoi to lash home a brilliant volley from 12 yards.
The Young Lions were in total control and doubled their lead just before the half-hour as Leeds loanee Nketiah continued his hot streak, hooking home from a corner.
The 20-year-old grabbed his second 11 minutes later as he headed home Dwight McNeil's inviting cross.
A brilliant opening 45 minutes was capped off in eye-catching style as Hudson-Odoi made it four with a fine goal.
He will take the plaudits as he ran the length of the field before finding the top corner from 20 yards, but his four team-mates who bombed forward at unbelievable speed also deserve credit.
It was job done for Boothroyd's side and they were unable to recreate the verve of the first half once the action restarted.
A rare attack from the visitors in the 66th minute ensured there would be no clean sheet as Baumgartner headed home from close range, but England finished on a high as Nketiah took the matchball home.
He was on hand to convert Rhian Brewster's low cross to make it six goals in four games for the Under-21s.
That should have been seven but his low penalty was well saved by Fabian Ehmann in the final five minutes after Brewster was fouled.