In your example, the objects are initially sorted by id, which makes the task pretty easy. But if this is not true in general, you can still sort the objects in linear time according to your array of id values.
The idea is to first make an index that maps each id value to its position, and then to insert each object in the desired position by looking up its id value in the index. This requires iterating over two arrays of length n, resulting in an overall runtime of O(n), or linear time. There is no asymptotically faster runtime because it takes linear time just to read the input array.
function objectsSortedBy(objects, keyName, sortedKeys) {
var n = objects.length,
index = new Array(n);
for (var i = 0; i < n; ++i) { // Get the position of each sorted key.
index[sortedKeys[i]] = i;
}
var sorted = new Array(n);
for (var i = 0; i < n; ++i) { // Look up each object key in the index.
sorted[index[objects[i][keyName]]] = objects[i];
}
return sorted;
}
var objects = [{id: 'Tweety', animal: 'bird'},
{id: 'Mickey', animal: 'mouse'},
{id: 'Sylvester', animal: 'cat'}],
sortedIds = ['Tweety', 'Mickey', 'Sylvester'];
var sortedObjects = objectsSortedBy(objects, 'id', sortedIds);
// Check the result.
for (var i = 0; i < sortedObjects.length; ++i) {
document.write('id: '+sortedObjects[i].id+', animal: '+sortedObjects[i].animal+'<br />');
}