I know that the United States and the Ottoman Empire were on opposite sides during World War I but that is the extent of my knowledge of US-Ottoman relations.
I'll try to answer your question, sorry if it doesn't satisfy you
A concrete proposition for a relations with the Ottoman Empire first proposed in 1786, when US treaty commissioners were interested in sending a mission to Istanbul during negotiations with the Dey of Algiers. However, Charles Gravier advised not to, arguing that the effort to undertook such mission would outweigh the benefits. The idea got floated again in the 1790s, with Rufus King convinced John Adams to establish relations with the Ottoman Empire. In 1799, Adams finally appointed William Smith as envoy to the Sublime Porte with the intention of establishing relations. However, this attempt was also foiled by the Napoleonic Wars, during which the Ottomans were allied with Britain and Russia to drive out Napoleon from Egypt and the Mediterranean so it was feared establishing relations with the Ottomans could jeopardize American-French relations. In the Ottoman Empire itself, the United States isn't entirely unknown - in 1800 the Porte accredited an American warship and subsequently established a treaty allowing American merchant ships to trade in Western Mediterranean.
After the Napoleonic Wars, negotiations was once again resumed, however Greek Revolt and the subsequent European alliance against the Ottomans at this time becomes a major obstacle to an establishment of relations. To circumvent this, Commodore John Rodgers of the Mediterranean squadron was ordered to hold secret negotiations with the Porte in 1825, however this failed to produce concrete results. However, the destruction of Ottoman navy in Navarino and the end of the war in 1829 resulted in an ideal situation for negotiation. On 7 May 1830, a team sent by Andrew Jackson finally concluded months of negotiations with the signing of an American-Ottoman treaty, which included trade negotiations and capitulations. The Ottoman-American Treaty of 1830 was very well received and marked the beginning of official relations between the United States and the Ottoman Empire, with an American Legation opened a year later in Istanbul. During the succeeding years Ottoman-American relations was rather uneventful, with it being dominated by trade and missionary activities, especially those conducted by the American Board of Commissioners for Foreign Missions (ABCFM)
During the American Civil War, the Porte supported the Union. In response to the appearance of Confederate privateers, on 26 March 1862 Sultan Abdülaziz issued an imperial decree prohibiting the entrance of privateers, which operated against American shipping and commerce, into the Ottoman waters and ports, a gesture of which was appreciated by the Federal government. The Porte also looked favorably on the Unionist victories during the Civil War, and even sent Ulysses S. Grant Arab horses as gifts. The Porte also sent condolences after the assassination of Abraham Lincoln. The first genuine crisis between the Porte and American government happened in 1895, after the brutal repression and massacres of Armenian revolutionaries which caused a public outcry in the United States, especially since the missionary effort was primarily directed towards converting Armenians. The Senate finally adopted a resolution to force the Porte to pay indemnities for American loss and injuries in the massacres and to provide information regarding the event, which was accepted in 1901. Additionally in 1899 during the Philippine insurrections, American minister Oscar Straus attempted to gain Sultan Abdülhamid II's support for the United States. The Sultan, probably driven by desire to placate the US government after the 1895 event sent a telegram calling for the Philippine Sulu Muslims to place themselves under American control, as their practice of religion would not be disturbed. Eventually the Sulu Muslims refused to cooperate with the insurrectionists, but i don't know the extent of it and whether or not the telegram actually influenced the matter. The Young Turk revolution of 1908 which ended Sultan Abdülhamid II's rule was received favourably by the American government. In 1909, driven by Howard Taft's dollar diplomacy policy, admiral Colby Chester and some entrepreneurs established the Ottoman-American Development Company (OADC) to construct railway lines in Eastern Anatolia. The company repeatedly tried to get their approval from the CUP government, but it produced no concrete results and it was eventually disbanded in 1911. During this time, Ottoman-American relations was highly characterized by trade, with the establishment of U.S. Chamber of Commerce for Turkey and the upgrade of Legation to Embassy supporting it. The value of goods exchanged dramatically rise from $560,101 in 1831 to $24,171,596 in 1914. Ottoman exports sharply rise during the Young Turk era, and by 1914, the value of Ottoman exports was almost seven times more than the American ones. Some of the commodities exported by the Ottomans were wool, rugs, hides, fruits, and opium, while the United States exported cotton, manufactured goods, machinery, and steel products.
Starting with the Ottoman entry into the war in 1914, the US-Ottoman relations were severely strained. After their entry, the Ottomans immediately abolished the Capitulations, which was protested by US ambassador Morgenthau protested and would not recognize a unilateral annulment of the Capitulations, which was a breach of 1830 treaty. The US maintained its capitulations policy officially until the end of the war and warned that the Porte would be held accountable for injuries to American citizens. The Porte informed further correspondence regarding Capitulations would be ignored, but they still want to avoid direct confrontations with the US and so while the Porte taxed American institutions, isolated incidents regarding the Capitulations were settled diplomatically to avoid crisis. The Armenian genocide further strained relations and stirred up the already anti-Turkish sentiments in the US. The State Department immediately protested to the Porte and even asked Germany to remonstrate against the treatment of Armenians, rallies were held in various American cities, and relief fund organizations like American Committee for Armenian and Syrian Relief were set up. With the American entry into the war in 1917, the United States and Ottoman Empire severed diplomatic relations, but both sides were unwilling to declare war. The Ottomans had no gains from declaring war to the US, while Woodrow Wilson was worried that a confrontation would damage American properties and institutions in the Empire. As such, stressing that the Ottomans Empire had committed no acts against the US, both President Wilson and Secretary Lansing held a firm position against attempts in Congress for declaration of war against the Ottoman Empire.