Villa opened the scoring through Helenius' near post header from Matt Lowton's cross on the hour mark following a quiet start to the game in the first half.
Wednesday night's game was the first in a three-match tour of Germany which will also see Villa take on SC Paderborn and VFL Bochum.
West Ham eased to a 3-0 win over non-league Boreham Wood in a pre-season friendly at Meadow Park.
The victory was the Hammers' second this week following a 6-2 win over League of Ireland Premier Division side Cork City on Tuesday.
Allardyce sent out a strong side against their Conference South opponents, with the likes of skipper Nolan, Joe Cole and new signing Razvan Rat all seeing action.
The Romanian was involved in the opener on 20 minutes when his cross was directed goalwards by home defender Ben Nunn. Keeper James Russell was forced into a reaction stop, but Morrison was on hand to pounce on the rebound to open the scoring.
Vaz Te made it two just a minute later, rising to nod home from Mark Noble's corner.
Allardyce rang the changes at half-time, with Matt Jarvis among those entering the fray, and the former Wolves winger proved a danger for the remainder of the match.
But it was Nolan who wrapped up the win, volleying home with seven minutes remaining.
West Ham are due to meet Bournemouth next week. The club begin their Premier League campaign against Cardiff City at Upton Park on August 17.