SPOILER!!!!!!!!! THIS WILL SPOIL THE END OF THE MOVIE!!!!!
The aliens were killed because they had no immune system against Earth's diseases as humans do. When we get sick, our immune system fights these diseases and forms immunity against them. But, these diseases weakened the aliens and in some cases even killed them. You remember the last alien? They mentioned the birds on him because the exterior shield these aliens had, was no longer activated and the birds could safely sit on him, showing he had weakened by Earth's diseases. Even the common cold could've killed these aliens.. because they had no defense against one thing.. our smallest organisms called 'germs'.
I understood it alot better because years ago I read the book, which was exellent. I'd recommend anyone to read the book.. it was truly a great read and explained the ending much better.