First of all, the broader issue is super complicated. There is no way we can cover it all here. No way. Take for instance: http://eprints.lse.ac.uk/745/1/Chapter8_Introduction.pdf [0]

Also, we are all wrong on certain points given certain assumptions. For instance, given the assumption that a state is defined as a political entity with absolute sovereignty, the 50 U.S. States could not be termed states. I'm very well aware of that and probably should not have been authoring a response a bottle of Zinfandel into the awesome "Fortitude" series, from Amazon.

I was fortunate to be able to take a class, "The State and Sovereignty", with Richard Ashley, who more or less wrote the book (or paper) on post-modern or post-structural International Relations [1]. From another site: "Ashley is concerned with how concepts like the state, sovereignty, and war are rarely questioned as problematic in international politics (Ashley 1989: 302). If the state is the central unit of analysis in IR and yet it is rarely thoroughly examined, how accurate are the assumptions that realism and liberalism rest on?" [2]. My thesis for this class was on this exact topic. Titled "Sovereignty: A Non-Sequitur", I used a lot of words to reference a lot of other people who used even more word to call bs on the very concept of state sovereignty.

But, hey, that's what you get when you approach a complex topic in a blunt fashion. But let's not stop now, let's go to Wikipedia:

State (polity) := "A state is an organized political community living under a single system of government. Speakers of American English often use state and government as synonyms, with both words referring to an organized political group that exercises authority over a particular territory. States may or may not be sovereign. For instance, federated states that are members of a federal union have only partial sovereignty, but are, nonetheless, states." [3]

Federation := "A federation (from Latin: foedus, gen.: foederis, "covenant"), also known as a federal state, is a political entity characterized by a union of partially self-governing states or regions under a central (federal) government. " [4]

"The component states are in some sense sovereign, insofar as certain powers are reserved to them that may not be exercised by the central government. However, a federation is more than a mere loose alliance of independent states. The component states of a federation usually possess no powers in relation to foreign policy, and so they enjoy no independent status under international law. However, German Länder do have this power, which is beginning to be exercised on a European level." [4]

U.S. State := "A state of the United States of America is one of the 50 constituent political entities that shares its sovereignty with the United States federal government. Due to the shared sovereignty between each state and the federal government, Americans are citizens of both the federal republic and of the state in which they reside.[3] State citizenship and residency are flexible and no government approval is required to move between states, except for persons covered by certain types of court orders (e.g., paroled convicts and children of divorced spouses who are sharing custody)." [5]

German Länder (States of Germany) := "Though international relations including international treaties are primarily the responsibility of the federal level, the constituent states have certain limited powers in this area: in matters that affect them directly, the states defend their interests at the federal level through the Bundesrat (literally Federal Council, the upper house of the German Federal Parliament) and in areas where they have legislative authority they have limited powers to conclude international treaties 'with the consent of the federal government'." [6]

[1] http://journals.cambridge.org/action/displayAbstract?fromPag...
[2] http://polisciprof.blogspot.com/2006/03/some-thoughts-on-pos...
[3] https://en.wikipedia.org/wiki/State_%28polity%29
[4] https://en.wikipedia.org/wiki/Federation
[5] https://en.wikipedia.org/wiki/U.S._state
[6] https://en.wikipedia.org/wiki/States_of_Germany

So, we have, at least as far as Wikipedia is concerned but surely others will say the issue is more complicated [0], that: federated states that are members of a federal union are indeed states, there is such a thing as state citizenship, and that states belonging to a Federation do enjoy independent status under international law.

Now, in practice, how do U.S. States feel about Trade agreements. Let me google that for you:

https://www.citizen.org/documents/States_Rights_and_Trade.pd...

https://www.citizen.org/documents/SovereigntyFactSheet09.pdf

http://leg.wa.gov/House/Committees/CDHT/Documents/JLOCTP.pdf

http://www.ncsl.org/ncsl-in-dc/standing-committees/labor-and...

It's a real issue, that is not always clear, that is becoming ever more important with treaties such as the TPP.

I don't know what else to give you.