The cemetry in Moedling is owned by the town and is open every day. The Jewish Cemetry in Moedling is part of the municipal cemetry and is therefore not locked. You enter the main entrance turn right and some 10 metres immediately next to the adminstration builing is the Jewish Cemetry. On each of my visits the gate was always closed but never locked. I have visited the cemetry several times and have photos of many graves. What is the name you are looking for ?
Moedling is a town in its own right and certainlt not a suburb or Vienna. The best way to reach Moedling is to take the train >from Wien Mitte. The cemetry is quite a way out of town and there is a bus but a taxi may be better.
The Jewish community of Vienna look after this section of the cemetry - it has been somewhat restored but is quite untidy. I do like it and visit it every time I go the Moedling - my parents home town