In what ways did enslaved peoples in the US respond to the inhumanity of their situation?

For enslaved people in the United States, and prior to that the Thirteen Colonies, there were a number of ways to respond to the inhumanity of slavery. Some actively resisted slavery, while others focused on attempting to improve spirits during such a difficult time.
One of the ways slaves could resist before being taken to the Americas from Africa was to run away from their captors. This would also be a way for slaves to resist and seek freedom in the United States. Once northern states began to ban slavery and Britain banned slavery from their empire, many slaves would escape slavery by heading to free states or to British-controlled Canada, where they would have freedom.
Another way slaves could resist slavery before being brought to the Americas was through suicide. For some enslaved people, an option to avoid slavery was to take drastic measures, such as jumping from a slave trading ship into the ocean. While this would result in the death of the individual, it would free them from a life of slavery.
Slaves had a number of other methods to resist slavery, in addition to running away. They would sometimes intentionally break or damage tools in order to slow down work and cause the tools to need repair or replacement. There are also instances of slaves faking illness to avoid having to work. Finally, slaves could intentionally slow down the speed of their work to hopefully cause lower profits for the slave owner.
One of the more extreme methods of opposing slavery would be through uprising or rebellion. Some examples of slave rebellions in the Thirteen Colonies and the United States include the Stono Rebellion and Nat Turner's Rebellion. Many slave owners had to confront the possibility of a slave uprising against them. This was, however, also dangerous for the slaves, because in most cases the uprisings were crushed, and the slaves involved could face harsh punishment—including death.
Finally, many slaves attempted to maintain African culture and traditions. This would involve things like drumming, which was central to African music, and practicing African religions. In many cases, this had to be done in secret, as it was often banned by slave owners. There is, however, no doubt that African culture and traditions, particularly in music, have found their way into the American culture we know today.
http://www.discoveringbristol.org.uk/slavery/against-slavery/black-resistance-against-slavery/slave-resistance-at-work/

http://www.discoveringbristol.org.uk/slavery/people-involved/enslaved-people/enslaved-africans/resisting-slavery/

https://www.pbs.org/wnet/african-americans-many-rivers-to-cross/history/did-african-american-slaves-rebel/

The enslaved status had many elements of inhumanity beyond the basic problem of denial of personhood. Conditions of enslavement varied through time and in different places so people's adaptations to conditions changed as well.
One fundamental feature was determination to resist the dehumanization of enslavement. This included maintaining and creating cultural forms that celebrated positive characteristics of African American peoples, including the African societies whence they came. Cultural forms included food, religious practices, music, and oral traditions.
In addition, acquiring new skills such as literacy in European languages, and writing and publishing in those languages was also important. Free persons of color, who were often formerly enslaved, wrote for abolitionist publishers and also lectured against slavery.
Enslaved people also found ways to leave slavery for themselves or family members. While voluntary manumission by owners did occur, more often slaves purchased their freedom. Skilled slaves who were hired out to work for wages sometimes were allowed to allocate a portion of the wage toward that purchase. Often the worker first purchased freedom for a child or an elderly parent, one at a time, and waited to gain their own freedom last.
Leaving slavery by escape became increasingly common in the 1850s-1860s, especially near the Mason-Dixon line and farther west, where the travel distance to a free state or territory was shorter. Escape into forested or swampy areas was well established during colonial times.
Accomodation and resistance were intertwined as armed rebellion was not only dangerous but took concerted planning, which was often hard to achieve. Small-scale uprisings, though each might affect a small number of people, were not unusual as a means to gain concessions from an owner.
https://nmaahc.si.edu/slavery-and-freedom

https://www.britannica.com/topic/American-Anti-Slavery-Society

Enslaved African Americans sometimes tried open revolt, such as Nat Turner's Rebellion in 1831, but this was put down violently and was quite rare.  Some African Americans escaped north to freedom, but this was rare too; many African Americans who escaped stayed in the South but hid from society.  The Underground Railroad assisted many slaves, but only a minority of slaves managed to escape.  There was just too many dangers involved in the trip.  A few slaves killed their masters, but this was rare as well. The penalty for this was a harsh death.  
The most common form of resistance was passive.  Slaves worked slowly or only partially followed directions.  Slaves stole or broke the tools needed in the fields.  Livestock were neglected.  While many plantation owners resorted to beating their slaves for these minor infractions, many more just said that the slaves were dumb.  This would lead to negative stereotypes that affected African Americans in the South.