In a 208Y/120 4 wire Wye system, you'll get 120 volts between either ungrounded (hot) conductor and the grounded (neutral) conductor. So if you're trying to connect a 120V appliance, all you need is one ungrounded (hot) conductor, one grounded (neutral) conductor, and one equipment grounding conductor.
The ungrounded (hot) conductor will connect to the brass colored screw terminal on devices (the small hole/blade), while the grounded (neutral) conductor will connect to the silver colored terminal (the larger hole/blade). The neutral conductor should never be connected to the equipment grounding conductor, or equipment grounding terminal on devices.
Notes:
Since it sounds like you're a bit over your head, you should probably contact a local licensed Electrician to finish the project and for any future electrical projects.
While you can solder connections in house wiring, it's not a common practice anymore. You'll also want to insure that you are using solder that is rated and labeled for the use, and that your solder joints are strong and insulated.
As one of the commenters pointed out, this is not 2-phase power (at least assuming something similar to standard U.S. residential 240V single-phase/split-phase service--what country are you in?). It's single-phase power. You get 240V between the poles on the smaller coil of the transformer outside your place. So you get 120V (half) from each pole to the exact center of the coil, where the "neutral" taps in (it's a single-phase center tap transformer). The neutral carries the imbalance between the loads on the two poles (power from one pole is opposite polarity and thus cancels out power from the other). So if there's exactly the same load on each pole, the neutral carries zero current, but it almost always carries some current.
So... yes, technically this would work. But where are you going to tap in? With what kind of device? Are you planning to connect a #8 and #12 wire with a wire nut? ;-)
As another commenter pointed out, you will end up with a 120V appliance running on a circuit protected by a 40A breaker. Since you can't legally put a 15A or 20A outlet on a 40A circuit, that definitely violates code. The device itself isn't going to draw any more current than it needs unless it has a short, but you can't legally wire in an outlet that the appliance cord will fit.
Your 37A calculation is 93% of the rating of the 40A circuit. U.S. NEC says you can't design a circuit with a continuous load over 80% of the circuit breaker's capacity. But "continuous" means full draw for longer periods of time than you are going to operate your stove.
And your cooler only draws about one Amp. So you might be okay there.
So... if you absolutely, positively can't or won't pull a new 120V 15A or 20A circuit from the panel, it sounds like the sanest option (from yet another commenter) is to redirect that 40A 240V circuit into a small subpanel.
I just now saw a little 2 space, 4 circuit 70A capacity subpanel/load center at a major box store's website for $15. Cheap.
Hopefully the cable you already have running to the stove has 4 wires (2 hot, 1 neutral, 1 ground).
The neutral (grounded) and grounding buses in the subpanel have to be disconnected from each other, the neutral bus has to be isolated from the metal box, and the grounding bus has to be bonded to the box. Otherwise, if there's a fault in the neutral, all your return current ends up on the ground and potentially energizes the box.
Your existing 40A two-pole breaker in the main panel is your master breaker for the subpanel, protecting the existing wire. Put a 40A two-pole breaker in the subpanel to feed the stove, and a 15A or 20A single-pole breaker to feed an outlet for the cooler.
You can use a masonry bit and concrete screws to drill and screw the little subpanel to the concrete, and to secure the conduit or MC that you'll run from that panel to the outlets for the stove and cooler. Which you will secure to the concrete in similar fashion.
You could use a small panel similar to this:
Best Answer
Its made to operate on 5-continent power, in which 400V "wye" 3-phase is delivered to the neighborhood, then each house gets 1 phase + neutral (230V), or more than one phase if load warrants. The device is designed to support using 3 phases separately, so they can be evenly loaded.
Whether this is well insulated enough to use in North American/Philippines split phase 240V, with no neutral and center-tap ground, is a question for the manufacturer.
And the manufacturer's reputation.
Note the sections of US NEC:
Your insurance company has a say too, if shabby, unlisted equipment caused your fire, they don't need to pay. That's why UL is called Underwriter's Laboratories.