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If you field an army with two warlords that both have warlord traits which one gets the benefit? I was under the impression that there can only be one warlord per army and that you have to choose. Is this correct? Also if a warlord with a warlord trait is in an army does it take precedence over a commander that has no warlord trait?

You cannot field an army with 2 warlords.

If you have an HQ model that comes with a warlord trait and yet have another model(from one of your primary detachments) that has a higher LD then you use or roll for trait per the Warlord rules from the highest LD. If the 2 are tied for LD(Character with warlord trait and non-character HQ); then you may decide which is the warlord(before rolling for traits on the non-character HQ).

From the BRB FAQ:

http://www.games-workshop.com/MEDIA_CustomProductCatalog/m3170233a_40K_RULEBOOK_v1.4_APRIL13.pdf
Q: If a model is listed as possessing a specific Warlord Trait in his
Bestiary / Army List entries, do the effects of that Warlord Trait
apply if the model is not nominated as your Warlord? (p111)
A: No.

As per page 111, you may only nominate one Warlord.

Ok so it is as I thought. Thanks guys.

When making an army list for a multi-game tournament, is it standard that you declare which is your warlord when you submit the list or can you change warlords between games?

As always when it comes to tournaments, it is the organizers that you need to ask that question to. They have the ability to change any rule away from the normal, and often have many internal processes when it comes to how the tournament is structured. One such internal process does often require you to submit your list ahead of time, and afterwards making it so you can not change any element on said list, but that is always up to the organizers of the event to decide.