To generate those nested, nearly identical `setTimeout` calls, instead of coding them all manually you could have a recursive function that builds and returns a function for you. Something like this would work:

    // Accepts an array of elements and a final callback function
    // Returns a function to show all elements and execute the callback
    function getFunctionToShowElements(elements, callback, currentIndex) {
        var i = typeof currentIndex === "undefined" ? 0 : currentIndex;
        if (i === elements.length - 1) {
            // at the final element, show the element and call the callback
            return function () {
                elements[i].fadeIn();
                callback();
            };
        } else {
            // for any preceding element, show the element and call a timeout
            var nextMethod = getFunctionToShowElements(elements, callback, i + 1);
            return function () {
                elements[i].fadeIn();
                setTimeout(nextMethod, 1000);
            };
        }
    }

Then you could set up a function for creating `audio` objects and attaching the event listener to fade in the given elements.

    function createAudio(filename,elements){
        var audio = new Audio(filename);
        audio.addEventListener("ended",function(){
            getFunctionToShowElements(elements,function(){sprite.play();})(); // get the function and execute it immediately
        });
        return audio;
    }

At this point you'll be able to create an `audio` object with the desired event handler like so:

    var audio = createAudio("audio/test.mp3",[element1,element2,element3]);

That's just to give you an idea of how you could go about cleaning it up. 

There are other improvements you'd want to make in your final code, such as using a variable for the timeout delay, and wrapping up the relevant code sections in closures as necessary. We'd need to see the full code to identify other areas for improvement.

Proof that the concept works:

<!-- begin snippet: js hide: true -->

<!-- language: lang-js -->

    var els = document.querySelectorAll(".showme");
    var sprite = {
        play: function () {
            alert("sprite.play");
        }
    };
    createAudio("audio/test.mp3", els);

    function createAudio(filename, elements) {
        var audio = document.querySelector("button"); //new Audio(filename);
        audio.addEventListener("click", function () {
            getFunctionToShowElements(elements, function () {
                sprite.play();
            })();
        });
    }


    function getFunctionToShowElements(elements, callback, currentIndex) {
        var i = typeof currentIndex == "undefined" ? 0 : currentIndex;
        if (i === elements.length - 1) {
            
            return function () {
                elements[i].style.display = "inherit";
                callback();
            };
        } else {
            
            var nextMethod = getFunctionToShowElements(elements, callback, i + 1);
            return function () {
                elements[i].style.display = "inherit";
                setTimeout(nextMethod, 1000);
            };
        }
    }

<!-- language: lang-css -->

    .showme {
        background-color:red;
        display:none;
    }

<!-- language: lang-html -->

    <button>Click me</button>
    <div class="showme">Number 1</div>
    <div class="showme">Number 2</div>
    <div class="showme">Number 3</div>
    <div class="showme">Number 4</div>

<!-- end snippet -->