Edrei was the second major battle of the Israelites against the Amorite kings in the region known as Bashan, ruled by king Og.
Numbers 21:33:
32. After Moses had sent spies to Jazer, the Israelites captured its surrounding settlements and drove out the Amorites who were there.
33. Then they turned and went up along the road toward Bashan, and Og king of Bashan and his whole army marched out to meet them in battle at Edrei.
34. The LORD said to Moses, "Do not be afraid of him, for I have handed him over to you, with his whole army and his land. Do to him what you did to Sihon king of the Amorites, who reigned in Heshbon."
35. So they struck him down, together with his sons and his whole army, leaving them no survivors. And they took possession of his land.
Deuteronomy 1:4:
3. In the fortieth year, on the first day of the eleventh month, Moses proclaimed to the Israelites all that the LORD had commanded him concerning them.
4. This was after he had defeated Sihon king of the Amorites, who reigned in Heshbon, and at Edrei had defeated Og king of Bashan, who reigned in Edrei.
Deuteronomy 3:1:
1. Next we turned and went up along the road toward Bashan, and Og king of Bashan with his whole army marched out to meet us in battle at Edrei.
2. The LORD said to me, "Do not be afraid of him, for I have handed him over to you with his whole army and his land. Do to him what you did to Sihon king of the Amorites, who reigned in Heshbon."
3. So the LORD our God also gave into our hands Og king of Bashan and all his army. We struck them down, leaving no survivors.
4. At that time we took all his cities. There was not one of the sixty cities that we did not take from them--the whole region of Argob, Og's kingdom in Bashan.
5. All these cities were fortified with high walls and with gates and bars, and there were also a great many unwalled villages.
6. We completely destroyed them, as we had done with Sihon king of Heshbon, destroying every city--men, women and children.
7. But all the livestock and the plunder from their cities we carried off for ourselves.
8. So at that time we took from these two kings of the Amorites the territory east of the Jordan, from the Arnon Gorge as far as Mount Hermon.
According to a few different references in the book of Joshua,
king Og "reigned in Ashtaroth and Edrei".
Joshua 13:31 called them his "royal cities".
Joshua 12:1-4:
1. These are the kings of the land whom the Israelites had defeated and whose territory they took over east of the Jordan, from the Arnon Gorge to Mount Hermon, including all the eastern side of the Arabah:
2. Sihon king of the Amorites, who reigned in Heshbon. He ruled from Aroer on the rim of the Arnon Gorge--from the middle of the gorge--to the Jabbok River, which is the border of the Ammonites. This included half of Gilead.
3. He also ruled over the eastern Arabah from the Sea of Kinnereth to the Sea of the Arabah (the Salt Sea), to Beth Jeshimoth, and then southward below the slopes of Pisgah.
4. And the territory of Og king of Bashan, one of the last of the Rephaites, who reigned in Ashtaroth and Edrei.
Joshua 13:8-12,29-31:
8. The other half of Manasseh, the Reubenites and the Gadites had received the inheritance that Moses had given them east of the Jordan, as he, the servant of the LORD, had assigned it to them.
9. It extended from Aroer on the rim of the Arnon Gorge, and from the town in the middle of the gorge, and included the whole plateau of Medeba as far as Dibon,
10. and all the towns of Sihon king of the Amorites, who ruled in Heshbon, out to the border of the Ammonites.
11. It also included Gilead, the territory of the people of Geshur and Maacah, all of Mount Hermon and all Bashan as far as Salecah--
12. that is, the whole kingdom of Og in Bashan, who had reigned in Ashtaroth and Edrei and had survived as one of the last of the Rephaites. Moses had defeated them and taken over their land.
...
29. This is what Moses had given to the half-tribe of Manasseh, that is, to half the family of the descendants of Manasseh, clan by clan:
30. The territory extending from Mahanaim and including all of Bashan, the entire realm of Og king of Bashan--all the settlements of Jair in Bashan, sixty towns,
31. half of Gilead, and Ashtaroth and Edrei (the royal cities of Og in Bashan). This was for the descendants of Makir son of Manasseh--for half of the sons of Makir, clan by clan.
There's mention of another town named Edrei in Joshua 19:37 when allotting towns for the tribe of Naphtali that would have been located on the west side of the sea of Chinnereth (later known as the sea of Galilee).