Region: Middle Earth
It can be found in the Unfinished Tales book, in the section "Cirion and Eorl and the Friendship of Gondor and Rohan"
You can also find it here
And in other resources online. Basically, the Oath of Eorl is an alliance between Rohan and Gondor, establishing the kingdom of Rohan. The kingdom of Gondor precedes the kingdom of Rohan, and the first steward of Rohan was the ruler of a group of men also called Eothed who were living somewhere more to the North-East, around Northern Rhovanion. They were roaming the plains and lived by breeding horses; they didnt have a kingdom of their own. At one time, Gondor was attacked from many directions, and the King of Gondor sent word to the Eothed folk to help, and they came to help with their horses and decisively won the fight as the enemy did not expect them and their powerful charge. So as a token of appreciation, the King of Gondor gave the plains north of Gondor, ie, Rohan, to the Eothed (under King Eorl) and it became their kingdom. In return, Eorl pledged eternal friendship and together they had this alliance and mutual help whenever in trouble.
The events of this are around 500 years prior to the events in the LOTR books and the War of the Ring, culminating with the destruction of the One Ring. It was renewed during the War of the Ring when Gondor asked for help from Rohan when Sauron attacked Minas Tirith (lighting the beacons etc) and Rohan came with their army of horsemen to the rescue.