Just to clarify, if instead of annexing Hawaii, America just declared war and took over by force, then you would not say the whole thing was illegal? It seems your suggestion that the annexation was illegal depends on technical language about annexation.
First of all, let me say the US and Hawaii are still in a state of war.
In affairs between recognized nation states, the relationship between them can only be in a state of war or peace. A state of war exists when one side declares war on the other or when one side commits acts of war without any declaration. Once war begins, a state of peace can only come about via a treaty of peace, which may or may not include any territory lost during that war. If there is no such treaty of peace, like in the case of the Korean War, there is no official end to hostilities and territory taken at the end of such hostilities is not official and can be described at occupied territories (e.g. West Bank, Gaza Strip, and the Golan Heights are illegally occupied by Israel).
In the case of Hawaii, the US did commit an act of war by participating in the overthrow of Queen Liliuokalani in 1893. After her being deposed, the so-called Republic of Hawaii was never recognized as the legitimate government by the US, as evidenced by the US not immediately annexing Hawaii as the Caucasian insurrectionists/traitors who instigated the overthrow of Liliuokalani had hoped and was the sole reason why they overthrew her at the very beginning. Fast forwarding to 1898, the US was getting into war with Spain and her colonies and the imperialist President McKinley wanted Pearl Harbor as a naval base to control the sea-lanes in the Pacific. He initially tried to annex Hawaii
LEGALLY via the US State Department, but was the vote to annex Hawaii was
DEFEATED in the Senate due to the famous Kue Petition that was presented to Congress showing Hawaiians did not want to be part of the US. Not giving up, the imperialists in US Government got Congress to draft and pass the Newlands Resolution in 1898, which President McKinley signed.
Since Congress has no jurisdiction to enact legislation of territorial acquisition, the annexation of Hawaii in 1898 is illegal based on US Constitutional Law.
Consequently, since no official treaty of peace or annexation exists, a state of war exists between the US and Hawaii and America's government / military presence in Hawaii as of date is illegal and can only be described as an illegal occupation.