In US residential systems, center grounded 120/240 service is the norm. In this arrangement, the distribution transformer on the utility pole drops the typically 12-18kV powerline voltage to 240V using a center tapped secondary. This is then fed to the home's breaker or fuse panel as Line 1, Line 2 and Neutral. Neutral is tied to earth ground at the service entrance (typically the panel, though it may be at a breaker outside at the meter box if the panel is some distance away). The voltage is 240V when measured from L1 to L2, and 120V from N to L1 and from N to L2. N to L1 and N to L2 appear to be 180* out of phase with one another, but are not really two phase because they come from the same transformer secondary.
Industrial settings are usually fed with three phase power; a common 'low voltage' (light industrial) arrangement is 120/208V 3 phase. (I say 'low voltage' because US industrial power may be 3 phase 120/208, 277/480 and I think in some instances 346/600) This is a 'wye' connection, with three 120V transformer secondaries, each with one end tied together (forming the 'neutral'). The primaries are each fed from one leg of the incoming three phase line, and the resultant output waves are 120* out of phase with one another. (L1, L2 and L3) Because they are 120* apart, they will measure 120V from line to ground, but only 208V from line to line (the phase differences mean that they do not add directly).
Single phase 120V AC circuits will usually have a hot (the line), a neutral and the ground (a protective earth). In normal operation, there should be no current flow in the ground; it is there only for safety. All current should flow through the line and the neutral wires only; they form the circuit. This may be either L1 or L2 and neutral in a single phase installation, or L1 or L2 or L3 to neutral in a 120/208 3 phase system.
In residential circuits where 240VAC is needed (for instance to power an oven or range, electric clothes dryer, or a large air conditioner), circuits may be two hots (L1 and L2) and a protective earth only. In 3 phase 208V settings, 208V may be derived from any pair of lines (L1 and L2, L2 and L3, or L1 and L3), with a safety connection to the protective earth line. (Again, in either the 240 or 208V scenarios, the earth ground should carry no current in normal operation - it is there to prevent the chassis of whatever it is connected to from going above ground potential in the case of a failure resulting in a short or leakage.)
AC distribution lines are not typically paralleled in my experience; if more current is needed then heavier conductors are run from the panel and a larger breaker is used.
How are you measuring resistance between hot and neutral - I'm assuming that you're doing this on the device to be powered, rather than the wires from the panel. Knowing what the device is would help to answer this question - things like incandescent lamps have very low 'cold' resistances and will appear to be near shorts if measured with an ohmmeter; once they are powered up their resistance increases with increasing temperature until they stabilize at their normal operating voltage and current.
Line to line will certainly work and provide a good sine wave without a neutral reference, but in that case both lines will be hot relative to ground. Ground and neutral in a properly wired circuit never share, though they are connected at the point where power enters the facility. From there on, they must be kept separate for safety purposes, even though they ultimately are connected together at that entry point.
Your upcoming power systems class should make all of this MUCH clearer - it is difficult to describe in type, but seeing schematic diagrams should help immensely in your understanding of it.
-Pat
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