As you have discovered, you won't be able to put PHP code into the body of a WordPress code and have the code run.
Your style variable is currently a string (enclosed in quotes). It needs to be an object. Remove the surrounding quotes. (Also, there is no need to escape the double quotes.) Try the following:
var style = {
baseUrl : "http://hella-stroh.de/jbgalleries/startseite/startseite/",
containerId: "juicebox-container"
};With regard to the common configuration options, the juicebox_style variable in your 'startseite.js' file is also currently a string rather than an object. It is not possible to add names to the Juicebox object as a string (like the PHP example). The PHP example slots in a chunk of text (server-side) before the code is parsed by the browser (client-side). The embedding code is fully formed (by the server-side PHP) before the browser even sees it. This is not the case with your JavaScript code.
Create an object with all your common configuration options (like the style object above) and then merge the two objects before feeding it to your new juicebox line. (You can keep the common configuration options object in your external JavaScript file but it should be an object rather than a string.)
For example:
var style = {
baseUrl : "http://hella-stroh.de/jbgalleries/startseite/startseite/",
containerId: "juicebox-container"
};
var common = {
autoPlayOnLoad: "TRUE",
showThumbsOnLoad: "FALSE"
};
for (var name in common) {
style[name] = common[name];
}
new juicebox(style);