in short, you need to retain a lawyer to look at this for you---this is not an insignificant amount of legal work.
The Copyright Act defines what is a "work for hire" in 17 USC 101. You cannot change the statute by private agreement. Generally what is done on elance is NOT a work for hire, despite the agreement expressly stating it is. However, the usual elance written agreement assigns copyright to the parting paying, so generally when you use elance you will obtain the copyright. It is doubtful that the Client will be deemed the author despite the express language saying so.
The specific wording is quite clear:
Ownership of Work Product and Intellectual Property
Contractor agrees that the Work Product is work made for hire. If any Work Product does not qualify as work made for hire, Contractor agrees that, upon Contractor’s receipt of payment from Client, the Work Product, including without limitation all Intellectual Property Rights in the Work Product, will be the sole and exclusive property of Client, and Client will be deemed to be the author thereof. If Contractor has any Intellectual Property Rights to the Work Product that are not owned by Client upon Contractor’s receipt of payment, Contractor hereby automatically irrevocably assigns to Client all right, title and interest worldwide in and to such Intellectual Property Rights. Except as set forth below, Contractor retains no rights to use, and agrees not to challenge the validity of Client’s ownership in, such Intellectual Property Rights. Contractor hereby waives any moral rights, rights of paternity, integrity, disclosure and withdrawal or inalienable rights under applicable law in and to the Work Product. "
So, to answer your specific question, it seems the elance agreement will fail in certain respects and work in other respects. If you need the precise detail as to the elance agreement you, as "Client", and the creator, as "Contractor", signed, then you need to hire an attorney. We cannot give you specific advice as to your agreement here, as you are not a client. We can only give general advice and inform you that you need to engage an attorney for specific advice.
Avvo is for finding and hiring a lawyer, not for avoiding hiring one. You would be very foolish to use advice here as a recipe for avoiding hiring an attorney.
I am not your lawyer and you are not my client. Free advice here is without recourse and any reliance thereupon is at your sole risk. This is done without compensation as a free public service. I am licensed in IL, MO, TX and I am a Reg. Pat. Atty. so advice in any other jurisdiction is strictly general advice and should be confirmed with an attorney licensed in that jurisdiction.