Dart lambda/shortland function confusion

In Dart => xxx is just a syntaxic sugar to avoid { return xxx; }. Thus the two following functions are equivalent :

var a = (String s) => s;
var b = (String s) { return s; } ;

You can also use => on method definitions :

String myFunc(String s) => s;
String myFunc(String s) {
  return s;
}

That syntax works well in a language like javascript and also c# where it supports (param1, param2, …, paramN) => { statements } with statement being separated with semi colon. In dart, the fat arrow only supports expression which is shorthand for { return expr; }.
That explains your Error. Your code with the curly brace (exp) => { print("Error occurred in class loading. Error is: $exp"); } means you are returning a map, so it expects to see something like (param) => {"key": "value"} where key is a string literal.

You need to choose either block syntax or single expression syntax, but not both.

You can't combine => with {}

Your two options are as follows using your example:

ClassWithFutures myClass = new ClassWithFutures();
myClass.loadedFuture.then( 
  (str) => print("Class was loaded with info: $str"),
  onErrro: (exp) => print("Error occurred in class loading. Error is: $exp")
);

or

ClassWithFutures myClass = new ClassWithFutures();
myClass.loadedFuture.then( 
  (str) { print("Class was loaded with info: $str"); },
  onErrro: (exp) { print("Error occurred in class loading. Error is: $exp"); }
);

In both cases, it is just a way to express an anonymous function.

Normally if you want to just run a single expression, you use the => syntax for cleaner and more to the point code. Example:

someFunction.then( (String str) => print(str) );

or you can use a block syntax with curly braces to do more work, or a single expression.

someFunction.then( (String str) {
  str = str + "Hello World";
  print(str);
});

but you can't combine them since then you are making 2 function creation syntaxes and it breaks.

Hope this helps.