What motivated the abolitionists? How did they try to persuade their audience to condemn the slavery in the American south? What were their most outspoken and most controversial points that they made?

The abolitionist movement was motivated by a number of factors that largely depended on the experiences and values of the individual. In some cases, abolitionists were motivated from personal experiences in slavery, such as Frederick Douglass. Abolitionists Granville Sharp and James Ramsey were motivated by encounters they had with slaves, in which they felt the treatment of slaves was not proper. The Quakers, one of the early groups to oppose slavery, were motivated by religious reasons. Abolitionists, as you can see, had various factors that motivated them to oppose slavery.
Abolitionists also used different tactics to persuade their audience to bring an end to slavery. Frederick Douglass famously spoke and wrote about the experiences of slavery. William Lloyd Garrison created a newspaper called The Liberator, which published anti-slavery information and images. Angelina Grimké Weld appealed to Christian women and mothers in the South. She asked women if, as mothers, they would allow their own children to be enslaved. Her argument focused on the fact that if nothing was wrong with slavery, then a mother should have no qualms about allowing her own children to be enslaved. Harriet Beecher Stowe created the novel Uncle Tom's Cabin, which quickly became popular in the North. Her novel included many significant scenes highlighting the horrors of slavery.
I would argue that the most "outspoken" would be those who did not merely use words, but instead used violence, in an attempt to achieve their abolitionist goals. John Brown, for example, is believed to have been involved in the murder of 5 proslavery men in the Pottawatomie Massacre. He also famously launched the Raid on Harpers Ferry. In the Raid of Harpers Ferry, Brown and his supporters captured a federal arsenal in Harpers Ferry, Virginia. Brown hoped that slaves in the area would come to support the raid and thus launch a larger slave rebellion in Virginia, however this did not occur. Brown would be tried for treason and executed for this action.
http://abolition.e2bn.org/slavery_56.html

http://utc.iath.virginia.edu/abolitn/abesaegat.html

https://www.kshs.org/kansapedia/john-brown/11731