Watching The Sound of Music, Captain Von Trapp has orders to enlist in the Kriegsmarine from the Austrian navy following the Anschluß. What actually happened to the Austrian armed forces? Were they folded into the German army or was there any attempt to distinguish them? Were there any hold-outs against unification with Germany?
The Austrian armed forces were incorporated into the Wehrmacht, and thereafter the Austrian populace was subject to German conscription laws. For example, the Wehrmacht 45th Division was originally the 4th Division of the Austrian army, reassigned to the Wehrmacht following the Anschluss and participated in campaigns from Poland in 1939 to Czechoslovakia in 1945.
It's also worth noting that despite Austria being afforded "victim status" by the Allies following WW2, many Austrians served in positions of high authority in the Nazi party, the Wehrmacht, and the SS, including some who were key participants in the Holocaust. In my opinion, it is best to consider Austria as simply part of Nazi Germany from 1938-1945.
To answer your second question, there was no national resistance movement against the Nazis in Austria. Part of the reason for this is that there was support among Austrians for the Anschluss (though far from universal), but probably more important is that the men of military age and experience were serving in the Wehrmacht, meaning both that there were fewer fighting men available to resist and that any resistance movement would face the additional psychological hurdle of having to fight their countrymen.