Working code sample.
Trivial markup:
<!DOCTYPE html>
<html ng-app="APP">
<head></head>
<body ng-controller="myController">
    <script src="angular.min.js"></script>
    <script src="controller.js"></script>
</body>
</html>
Trivial code sample:
angular.module('APP', []).controller('myController', function($scope) {
    $scope.test = function() {
        console.log('Weird behaviour!')
    }
    (function() {} ()); //if you comment self-executing function console will be empty
});
And really strange scope behaviour. Can you please explain why this happens?
You've unintentionally made test scope method IIFE, and the current code is essentially
$scope.test = (function() {
    console.log('Weird behaviour!')
})(undefined)
While $scope.test itself will be undefined.
It should be
$scope.test = function() {
    console.log('Weird behaviour!')
};
(function() {} ());
Semicolons are precious.
As you added code write after $scope.test function, It has () to it. So because of that it is test function is considered as self executing function,
As @estus already said you could avoid that issue by ending your function code by ;.
Code
$scope.test = function() {
    console.log('Weird behaviour!')
}(function() {} ())
                        Other answer for semicolon-haters:
 $scope.test = function() {
   console.log('Weird behaviour!')
 }
 !function(){}();
It's general rule to escape your startline [/('s when you write semicolon-less style:  
;[].forEach.apply(arguments, iterator)
;(function(){})()
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