Taking longer than I thought it would be, but here it is.
The complete list of insert songs [minus the three No Name songs] by order of appearances:
Title [Japanese] - [Episodes appeared] - [Origin]:
Spoiler for Complete List of insert Songs:
Aitakatta[会いたかった][EP 01,03,08,09][Debut (1st) Single, 3rd counting underground/private labels]
Shōjo-tachi yo[少女たちよ][EP 01][From 1st Original Album, theme song for DOCUMENTARY of AKB48 to be continued]
Shonichi[初日][EP 01,04][1st song from B3 (Team B 3rd Stage: Pajama Drive, it is also Team B's first original stage), C/W song for 12th Single)
AKB Sanjō![AKB参上! ][EP 02][14th song (1st encore song) from A5 Stage: Ren'ai Kinshi Jōrei]
Heavy Rotation[ヘビーローテーション][EP 02,04,09][17th Single]
Beginner[Beginner][EP 03,08][18th Single]
Ponytail to Shushu[ポニーテールとシュシュ][EP 03][16th Single]
Lemon no Toshigoro[檸檬の年頃][EP 04][Opening song by Trainees from K6 Stage:Reset]
Manatsu no Sound Good[真夏のSounds good!][EP 06][26th Single]
Anti[アンチ][EP 06][C/W song from 21st single, theater edition, Trainee song]
RIVER[River][EP 07,09][14th Single]
Ougon/Golden Center[黃金センター][EP 07][C/W song from 20th single, theater edition, Trainee song]
Heart Gata Virus[ハート型ウイルス][EP 09][6th song from A5 Stage: Ren'ai Kinshi Jōrei, 1st Album for sub-group NO3B]
Namida no See-Saw Game[涙のシーソーゲーム][EP 09][C/W song from 17th single, Type-B]
Sasae[支え][EP 09][16th song (3rd encore) for K4 Stage: Saishū Bell ga Naru]
To be continued[To be continued][EP 11][16th song (3rd encore song) for K4 Stage: Saka Agari]
Nagisa no CHERRY[渚のCHERRY][EP 11,12,13][4th song from A2 Stage: Aitakatta]
Ōgoe Diamond[大声ダイヤモンド][EP 12][10th Single, consider as the turning point song for the group]
Yakusoku yo [約束よ][EP13][12th song (1st encore) from K2 Stage: Seishun Girls]
That a total of 19 songs not counting the three from No Name. For live footage, it should be fairly easy to find on youtube with either name. The name of stage reflects the songs it is under, those interested in other stage songs and search under stage name. For full track on stages, feel free to ask in AKB Thread.