Two-conductor Romex wire, by its design, creates a parallel circuit between all junction boxes on the circuit that are connected by Romex. Usually, an electrician wiring a house will start at the closest box to the panel, and run a length of 14/2 or 12/2 back to the panel. Then he will run additional lengths (there are code restrictions on how many Romex bundles can come into particular types of J-box, see here) from the node connected directly to the panel out to other nodes, "daisy-chaining" them together node to node (this is especially true for outlets; he'll simply drill holes through the 2x4 studs if the wall hasn't been drywalled yet, and feed the line horizontally from outlet box to outlet box). Then, connecting black to black (sometimes on opposite ends of a light switch) and white to white will put all of the things that receive power from this circuit in parallel, with the exception of switches, which are in series with whatever they control.
So, without any knowledge of your house's actual wiring other than what you've told me, my guess is that the wire comes out from the panel, to either the switch or one of the outlets, and then there is another line whose wires are connected to the same or continuous terminals on the switch or receptacle, and lead to another switch or receptacle. Knowing how these nodes HAVE to be connected in order to work, you are either missing 2 Romex bundles in your picture (there should be an extra bundle leading into two of these device boxes), there is an additional device box that is on this circuit which you have not put in the image, or there is a junction point which you can't see at which the bundles from one or more of these endpoints are spliced with the line back to the panel.
One more tool you may find useful to diagnose this, in addition to your NCVT and plug tester, is a line tracer. A line tracer is much like a breaker finder (in fact a breaker finder can usually be used for this purpose) but usually is much more sensitive, but cannot be used on energized wire (usually line tracers are used in IT/data applications to identify particular data cables). It consists of a tone generator that plugs into a receptacle, and a probe that senses the EM tone being output into the wire by the generator. You can plug the generator into one of the receptacles you know is on a particular circuit, then take the probe and trace the line from the J-box to wherever else it may go. What you're looking for are places where the line "tees"; the probe can sense wires leading off in more than one direction from a particular point, AND that point isn't at a faceplace or other installed, removable electrical device of some sort. That tee is a junction point, containing the wire splice that connects the various endpoints. If you cannot access that junction, either by removing the faceplate right in front of you or by going into the attic above you, then you have an illegal junction point. You need to expose that wire junction, and if necessary put it into a proper box, and ensure that the junction is fully continuous (and that you can read 110V from at least one wire in the junction).
Let's see if I can draw this all once again...
CAVEAT: I'm an electrical engineer, not an electrician. My description of the circuits will be correct, but someone should double-check me on the color-coding conventions.
The basic concept of a three-way circuit is that you have two single-pole, double-throw switches hooked up back to back:
Switch 1 Switch 2
Black .___________Black Traveler_____________. Black
Hot ____./ .________ Switched Hot to load
.___________Red Traveler_____________./
White White
Neutral_______________White Neutral________________________ Neutral to load
Green or bare Green or bare
Ground _______________Green/bare ground____________________ Ground to load
When both Switch 1 and Switch 2 select the Black Traveler, or both select the Red Traveler, current flows and the load is powered. When they don't agree (one selects BlackT and the other selects RedT), current can't flow and the load gets no power.
The most common error made when connecting these is to get one of the switches "backward", connecting its common to one of the travelers. This results in a circuit that looks like:
Switch 1 Switch 2
.___________Black Traveler__________________
Hot ____./ .__)
.___________Red Traveler_____________. Black Switched Hot
\._________ To Load
White White
Neutral _______________White Neutral________________________ Neutral to load
Green or bare Green or bare
Ground _______________Green/bare ground____________________ Ground to load
Now, if Switch 1 is up (BlackT), then it doesn't matter which way Switch 2 is set, since there's no way current can get from the top of Switch 2 to the bottom (they can't both be selected at once) and the load gets no power. If Switch 1 is down (RedT), and Switch 2 is up (BlackT), both travelers are now hot, but there's still no power to the load. Only if both switches are down, connecting hot to RedT and RedT to the load, will current flow.
"Oops."
The fix, of course, is to figure out which switch is hooked up incorrectly and turn it around so it faces the right way. If the circuit has been properly color-coded (in the US, that means the travelers are black and red; it doesn't much matter which is which), you can tell this by inspection; each switch should have a black wire connected to its common, and a black and red (from the same cable) connected to its other two terminals. So if you can determine which of the two cables the red belongs to, you can see which switch is hooked up incorrectly and fix it immediately.
If you can't figure out which black belongs to the same cable that the red does, in either box, don't panic. Assuming that both switches do have a red and a black at their outputs, what has almost certainly happened is that the installer picked the wrong black for at least one of the switches. Swap the blacks at one switch (you DID turn off the breaker before opening the switch box, right?!?), turn the breaker back on and see if the switches now work as intended. If not, turn the breaker back off and swap the blacks at the other switch; turn the breaker back on and try again. If it STILL doesn't work as expected, turn the breaker off one more time, go back to the first switch and put the blacks back the way they were; this is the only remaining possibility and when you turn the breaker on one last time it should (finally!) work.
If it still doesn't work as intended, you've got a malfunctioning switch or bad wiring, and you should probably go after it with a multimeter or voltage probe to figure out which. Of course you could have used a probe earlier and saved yourself all the experimentation, but I've been presuming all that's available is a screwdriver and patience and the Mark 1.0 Eyeball.
Note: If you don't see the expected color coding -- one cable having black and white wires, and the other having black, white, AND RED wires -- STOP and find out what your country's conventions are for this, and/or figure out how the weirdo who set this up actually wired it.
There's one other complication, though.
I've been describing the most common setup, where the load is connected to the second switchbox. You can confirm that by the fact that there are two cables coming into each box, each switch has a black at common and a black and red as the two travellers, and the two whites (neutrals) in each box are connected to each other (so neutral runs alongside the travelers and is available in the second box for connection to the load).
Sometimes, however -- typically when the second switch was added later -- the load is actually connected at the first switchbox rather than the second. In this case, what you'll see is THREE cables coming into one box (Switch A) and ONE cable coming into the second box (Switch B). This winds up looking like:
Switch 1 Switch 2
Black .___________Black Traveler_____________.
Hot ____./ .________
.___________Red Traveler_____________./ \
White )
Neutral____ _____Return Traveler_______________________ /
| |
White Black
Neutral Switched hot
TO LOAD
Ground
Ground ______|________Green/bare ground____________________ Ground
OK, that works... but now we need to figure out what color the Return Traveler should be. The US-standard three-wire-plus-ground cable only gives us the four colors we've mentioned: Black for hot, White for neutral, Red for "alternate hot", and Green for safety ground. We don't want to have to buy another kind of cable just for this uncommon usage...
So there is, essentially, a Standard Cheat. In this setup, the Return Traveler uses the white wire in the traveler cable, BUT the electrician is Morally Obligated, On His Honor As A Member Of The Guild, to tag it with red electrical tape (or hit it with a red marker, at least!) at both ends so the next guy to open the box knows that it is intended to be a Second Alternate Hot -- another "red" -- rather than a neutral.
(Of course gods only know whether homeowner-installed circuits have been properly labelled this way. You can hope that the guy who was there knew what he was doing and left you this indication, but don't bet your life on it!)
The same problem of a reverse switch (or two) can occur in this case, of course. But now it should be a bit more obvious how to correctly hook up Switch Two, since the common should be this Second Alternate Hot... so if one of the switches is backward it almost has to be Switch One. And if that isn't the cause, as above, start checking that the switches actually work and that the wiring is intact.
Whew.
There will be a quiz next Thursday. If you have any questions, please ask your TA during the recitation section. I'm gonna go get a cold bubbly.
(One advantage us old farts have: We still remember how to draw ASCII graphics!)
Best Answer
As drawn, your left switch will operate your switched outlets, the right switch will operate the lights attached to the top-right cable, and any lights attached to the top-middle cable will be always-on.
Assuming what you want is for the left switch to operate the lights attached to the top-middle cable, the right switch to operate the lights attached to the top-right cable, and for the outlets to be always-on, you need to connect things more like this:
I've not drawn neutrals or grounds. All the white wires should be connected together; they will all be acting as neutrals. The grounds should be connected as in your original diagram.