HEAVY SPOILERS, PLEASE READ WITH CAUTION.
Adam was the very first Angel. Adam was not defeated but was captured in Antarctica where all his energy was used to initiate the 2nd Impact. During the process, Adam was reverted into embryo status and later transferred to NERV Japan. Adam is similar in appearance to the EVAs which are probably clones of Adam.
Lillith is the being where all life originated. In other cultures she is a fallen angel or Adam's wife before Eve. There is much confusion as to when and how NERV managed to obtain Lillith. She is vital to the EVA series - her blood is LCL, her body was used to create Rei and Unit 01. She is the vessel for the 3rd Impact and in case she was ever destroyed, Unit 01 was created from her as an alternative.
Sachiel is the first Angel encountered by NERV and the EVA series. It has many attack methods - a palm saber, a laser emitted from the eyes, physical strength, hovering and self destruction. Sachiel is also the Angel of Water.
Shamshel is powerfully armed with 2 electric whips. It was destroyed when Unit 01's progressive knife penetrated the core. After the battle, the 4th Angel provided a perfect specimen for NERV and although its core was damaged, it provided a model for the S² Engines later seen in Units 05 to 13. It was speculated this its S² Engine was transplanted into EVA Unit 04. Shamshel is also the Angel of Day.
Ramiel had the most powerful AT-Field of all the Angels. It was capable of deflecting attacks and also produced high energy outputs to attack anything that came within range. Ramiel was defeated by utilizing all of Japan's energy reserves channeled through the SSDS Positron Rifle. This was successful in penetrating the AT-Field and the core of the Angel. Ramiel is the Angel of Thunder.
The 6th Angel was encountered whilst EVA Unit 02 was being transferred to NERV Japan. Asuka and Shinji co-operated in defeating this aquatic Angel by opening its jaws allowing 2 destroyers to enter and fire at the core within the Angel to destroy it. Gaghiel is the Angel of Fish.
This was the first Angel that was capable of operating as 2 separate entities after Unit 02 sliced it in half. After defeating both Units 01 and 02, the Angel was partially destroyed using an N² Mine. The Angel was eventually destroyed by using synchronized attacks on both halves. Israfel is the Angel of Art.
The 8th Angel was detected within a volcano in the embryonic stage. When an attempt to capture it was made by Unit 02, it broke loose from the electromagnetic cage. The operation was immediately changed from capturing the Angel to destroying it. It was destroyed by the principle of thermal dynamics when Asuka used coolant to weaken the Angel's molecular structure. Sandalphon is the Angel of Birth.
Matarael is a spider-like Angel which attempted to attack NERV HQ during a power failure with acid secreted from its main eye. It was destroyed by all 3 EVA Units each taking a different position - Shinji as offense, Asuka as defense and Rei as the back-up. Matarael is the Angel of Seasons.
This gigantic Angel showed incredible intelligence. It was able to focus its AT-Field to jam satellite transmissions and also to drop and aim bombs from its orbit. Eventually it began to plummet to Earth where the 3 EVAs were in position to intercept it. Sahaquiel is the Angel of Sky.
Iruel is composed of thousands on nanomachines. It attacked during a synchronization test. Iruel was able to evolve and hack into the MAGI system before being intercepted by a program engineered by Ritsuko and Maya. Iruel is the Angel of Fear.
The actual Angel is a Sea of Durac. It is a giant shadow 600 km in diameter and 3 nanometres in thickness. Within this layer is an inverted AT-Field which works as a black hole. The physical shape in the sky is the shadow of the Angel. It was destroyed by Unit 01 after being swallowed by the Sea of Durac. Leliel is the Angel of Night.
Bardiel is actually the slimy substance located in the joints of Unit 03 which prevented the entry plug from ejecting. It actually attached to Unit 03 when it was being transported by a carrier which flew through a cloud, causing a brief shock of electricity. It possessed Unit 03, which at the time was piloted by Touji, and was destroyed by Unit 01 under the control of the Dummy Plug. Bardiel is the Angel of Blood.
Zeruel is one of the most powerful Angels. It had 2 razor sharp ribbon arms and incredibly powerful optic blasts which can penetrate 18 layers of armor protecting NERV HQ. It quickly disabled Units 02 and 00 but was defeated by Unit 01 which went berserk and devoured the Angel's S² Engine. Zeruel is the Angel of Might.
Arael had no intention in finding Adam. It simply wanted to understand the human mind therefore violating and desecrating Asuka's mind. It was beyond the range of any weaponry and thus was destroyed by using the Lance of Longinus. Arael is the Angel of Birds.
This Angel had no core. It is composed of a ring structure made from a double helix. It's attack method was to assimilate with an EVA. It was able to make contact with Unit 00 and also to communicate with Rei's mind. It was destroyed when Rei sacrificed herself and self destructed Unit 00. Armisael is the Angel of the Womb.
Kaoru/Kaworu Nagisa, the "5th Child", is the 17th and last Angel as written in the Dead Sea Scrolls. He was able to synchronize with Unit 02 immediately, taking the EVA with him into Central Dogma in search of Adam to initiate the 3rd Impact. Shinji was sent to stop him in Unit 01 and eventually, Kaoru wished to die and was killed by Shinji.