Entering EU when you have a Work Visa

Just to clear something up, not sure what Zurich has to do with Austria as its in Switzerland. Are you flying into Zurich from the States?

Well, the chances are you will not be asked anything at customs are very slim, but if you are, be truthful, and say that the reason for your travel due to work. It will not harm having a copy of your visa with you.

Providing you have all your documents there should be no reason do anything at the Embassy before you go.

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ARRIVING IN AUSTRIA
2.1 Duty of Registration
Residential registration is mandatory in Austria. Any person establishing their residence in Austria
(or moving their place of residence within Austria) is obliged to register with the respective competent
authority within three (3) days of establishing the residence.
Responsible authorities to contact in this regard are:
     •     registration office at your place of residence (municipality office (Gemeindeamt) or in cities
municipal district authority (Magistrat))
     •    in Vienna: the registration office of the municipal district offices (Magistratische Bezirksämter)
The following documents are to be furnished:
 completed registration form (Meldeformular) for each person to be registered; the registration
form can be obtained from the responsible registration authorities, in some newsagents/
     tobacconists (Trafik) or the Internet
     passport and birth certificate
     residence registration certificate(s) (Meldeformular(e)) for any other places of residence
The residence registration form (Meldeformular) must be signed by the lessee (the property owner
or the property management) and the residing person (e.g. tenant), submitted personally or by a
person of trust or sent by post to the responsible residence registration authorities (Meldebehörde).
The authorities issue a registration confirmation certificate (Meldebestätigung).
Note: you do not have to specify your religion on the residence registration form and you can leave
this category blank.
Upon registering in Austria, your personal data will be automatically saved in the Central Residence
Registry (Zentrales Melderegister (ZMR)) and available to authorities. Every person registered
in Austria is assigned a dedicated number in the Central Residence Registry (Central Residence
Registry Number, “ZMR-Zahl”) which is shown on the residence registration confirmation certificate
(Meldebestätigung).

Just an update... the only travel issue that I had was at Checkin in Los Angeles, where they wanted to know why I didn't have a return ticket...  I explained I was going to Austria for work and that my visa had already been approved, just not issued until I registered in the town where I will be living (Frastanz)... It helped to have a letter to that effect too, as well as a signed employment contract. But there were no other problems.... they just stamped my passport in Dusseldorf without any problem and I transferred to my domestic flight to Zurich without any problems.