Oi. 
This is actually more difficult than it looks because the Onkyo has to be configured carefully for these inputs. If everything was HDMI it would be easy, but you actually only have one input that's going to be HDMI (the U-verse box). Everything else is something older, and the Onkyo doesn't come pre-configured for that.
OK, you ready? Here we go.
Connections
1. Onkyo AV Receiver to Philips TV: Use HDMI cable from Onkyo HDMI Out port to Philips TV HDMI Input 1 port. Use HDMI cable (Monoprice, $3.50).
2. U-Verse Receiver to Onkyo AV Receiver: Use HDMI cable from U-Verse Receiver HDMI Out port to Onkyo HDMI In 3 (Cbl/Sat) port. Use HDMI cable, same as in #1.
3. Sony DVD to Onkyo AV Receiver: Use Component (3x RCA, red/green/blue labeled Y/Pb/Pr) + Digital Audio cable (1x RCA). For the 3x Component cable, go from Sony DVD Component Out jacks (3x) to Onkyo Component In 1 jacks (3x). For the digital audio cable, go from Sony DVD Digital Audio Out jack to Onkyo Digital In Coaxial 1 jack. Use 3x component cable (Monoprice, $2.95) and 1x digital audio cable (Monoprice, $1.28).
4. Sony VCR to Onkyo AV Receiver [This connection is for playback of tapes only]: Use Composite+Audio (3x RCA, red/white/yellow) from Sony VCR Output jacks (3x) to Onkyo VCR/DVR In jacks (3x). Use 3x Composite cable (Monoprice, $2.95).
5. U-Verse Receiver to Sony VCR [This connection is for recording of TV programs on the VCR, you can skip this connection if you don't need to do this]: Use Composite+Audio (3x RCA, red/white/yellow) from U-Verse receiver Composite Output jacks (3x) to Sony VCR Input jacks (3x). Use same cable as #4.
6. Teac 5-CD Changer to Onkyo AV Receiver: Use L/R audio cable (2x RCA, red/white) from Teac Output jacks to Onkyo AV Receiver TV/CD In jacks (2x). Use 2x RCA audio cable (Monoprice, $3.59).
7. Fisher Tape Deck to Onkyo AV Receiver: Use L/R audio cable (2x RCA, red/white) from Fisher Output jacks to Onkyo Game In jacks (2x). Use same cable as #6.
8. Onkyo AV Receiver to Bose 901 Speakers: Use standard speaker wire from Onkyo Front Speaker L + and - to Bose 901 Left speaker, and Onkyo Front Speaker R + and - to Bose 901 Right speaker. You will not be using the 901's equalizer in this setup.
Configuration
Now we have to configure several of these components to do what we want:
1. Sony DVD player, configure for progressive output: On the back of the Sony DVD player is a slide switch for Normal output or Progressive output. Set it to Progressive.
2. Configure Philips TV:
2a. Set input for HDMI 1: Power on the TV, press the Source button on the remote until you are selected to the HDMI 1 input.
2b. Turn built-in speakers off: Press Menu -> Sound -> TV Speakers -> turn OFF.
2c. Set picture format to Normal: Press Format -> select Normal -> press OK.
3. Configure the Onkyo [this is a pain]:
3a. Configure output resolution: On the Onkyo remote, press Receiver -> Setup -> select Input/Output Assign -> Enter. Select Monitor Out -> Enter. Select Auto -> Enter.
3b. Configure input mappings: On the Onkyo remote, press Receiver -> Setup -> select Input/Output Assign -> Enter. Select HDMI Input -> Enter. Set each setting as follows:
BD/DVD: -----
VCR/DVR: -----
CBL/SAT: HDMI3
GAME: -----
(Leave remaining selections at their defaults)
3c. Configure more input mappings: On the Onkyo remote, press Receiver -> Setup -> select Input/Output Assign -> Enter. Select Component Video Input -> Enter. Set each setting as follows:
BD/DVD: IN1
VCR/DVR: -----
CBL/SAT: -----
GAME: -----
(Leave remaining selections at their defaults)
3d. Configure yet more input mappings: On the Onkyo remote, press Receiver -> Setup -> select Input/Output Assign -> Enter. Select Digital Audio Input -> Enter. Set each setting as follows:
BD/DVD: COAX1
VCR/DVR: -----
CBL/SAT: -----
GAME: -----
TV/CD: -----
(Leave remaining selections at their defaults)
3e. Configure speaker settings: On the Onkyo remote, press Receiver -> Setup -> select Speaker Setup -> Enter. Select Speaker Settings -> Enter. Set each setting as follows:
Speaker Type: Normal
3f. Configure more speaker settings: On the Onkyo remote, press Receiver -> Setup -> select Speaker Setup -> Enter. Select Speaker Configuration -> Enter. Set each setting as follows:
Subwoofer: No
Front: Full Band
(Leave all other settings at their defaults)
3g. Use the Onkyo's built-in equalization mechanism to apply room-specific and speaker-specific settings: Follow the directions in the Onkyo's manual on pages 23 and 24 to to use the Audyssey 2EQ system with the calibrated microphone supplied with the Onkyo.
4. Configure U-Verse receiver:
4a. Configure output resolution: Select CBL/SAT on the Onkyo Remote to select the U-Verse receiver, and turn the U-Verse receiver on. Menu -> Options -> System Options -> Aspect Ratio -> Set to 1080i on high-definition screens.
4b. Configure digital audio output: Menu -> Options -> Audio/Language Options -> Digital Audio Output -> Set to Surround
4c. Configure aspect ratio: While watching TV, hit Enter (key below the 9 on the remote) -> Use L/R arrows to go to Zoom, set to Normal.
Operation
You can select which item you want to watch/listen to using the Onkyo's source selection buttons:
BD/DVD: Sony DVD Player
VCR/DVR: Sony VCR
CBL/SAT: U-Verse receiver
GAME: Fisher Tape desk
TV/CD: Teac CD changer
You have many audio listening modes available on the Onkyo, you will have to try them to see which sounds best with the Bose speakers. Check the Onkyo manual pages 28-32 for information on the listening modes. You may need different listening modes for different components.
