You can tag them all to ORD (technically if the layover in LAX is <24 hours, but in fact it would be better if it is <12 hours, per oneworld's website http://www.oneworld.com/ow/airports-...for-travellers). When you arrive in LAX, take the one(s) that you need to the hotel, and drop the other one(s) to the belt right after clearing customs in TBIT. If CX were able to issue you the boarding pass for the AA segment, all you need to do is to drop the one(s) you take to the hotel in T4 when you take your AA flight. If CX weren't able to issue you the boarding pass for the AA segment, remember to show all the baggage identification tag (including the one(s) you drop in TBIT) to the AAgent to ensure that they have the information in their system.

On another note, bags do get lost! This risk always exists. However, if the bag is tagged to ORD, and you've taken them in TBIT and either dropped them in TBIT after customs or in T4, then AA (the final segment's operator) would take all the responsibilities per IATA rules. Of course, if any of your bags didn't appear when you were in LAX, let a CX representative know.