If you have trouble getting into Budapest Keleti station (as has been the case last week), all trains to Vienna also stop at Budapest Kelenföld, unbeknownst to most refugees so there is no problem getting into the station there. You can easily get there by metro. That is, if trains are running again until then!
If not, you will have to make your way to Hegyeshalom and change to the Austrian trains there, as they are currently not being continued to Budapest. This might change any day though. If you are still forced to make your own way to Hegyeshalom I'd recommend a bus as trains will require multiple very complicated and unpredictable changes. Austrian railjets are operating normally from Hegyeshalom. Austrian Federal Railways is also currently offering refunds on all tickets to and from Hungary that have been bought from them.