There is no direct connection from Stratford to Wandsworth. However, you can take the Tube to London Waterloo then take the train to Wandsworth Town. Alternatively, London Underground (Tube) operates a vehicle from Stratford to Wandsworth every 10 minutes. Tickets cost $5 - $7 and the journey takes 51 min.
From Stratford Underground Station Tube to London Waterloo then train to Wandsworth Town. 35 min £8. From West Ham Underground Station Tube to East Putney Underground Station. 51 min £4. From Stratford taxi to Wandsworth. 25 min £49. From Stratford drive to Wandsworth. 25 min £2. From Stratford Uber to Wandsworth. 25 min £23. From Stratford Station, Stratford Bikeshare to Ram Street, Wandsworth. 1 h 23 min.