Yes, NM cable can be in conduit. In fact. NEC calls for it to be in conduit, when protection from physical damage is required.
National Electrical Code 2011
ARTICLE 334 Nonmetallic-Sheathed Cable: Types NM, NMC, and NMS
II. Installation
334.15 Exposed Work. In exposed work, except as provided in 300.11(A), cable shall be installed as specified in 334.15(A) through (C).
(B) Protection from Physical Damage. Cable shall be protected from physical damage where necessary by rigid metal conduit, intermediate metal conduit, electrical metallic tubing, Schedule 80 PVC conduit, Type RTRC marked with the suffix -XW, or other approved means. Where passing through a floor, the cable shall be enclosed in rigid metal conduit, intermediate metal conduit, electrical metallic tubing, Schedule 80 PVC conduit, Type RTRC marked with the suffix -XW, or other approved means extending at least 150 mm (6 in.) above the floor. [ROP 7-94] Type NMC cable installed in shallow chases or grooves in masonry, concrete, or adobe shall be protected in accordance with the requirements in 300.4(F) and covered with plaster, adobe, or similar finish.
There's also some notes in Chapter 9, dealing with how to figure for cables when calculating conduit fill.
Chapter 9 Tables
Notes to Tables
(5) For conductors not included in Chapter 9, such as
multiconductor cables and optical fiber cables, the actual
dimensions shall be used.
(9) A multiconductor cable, optical fiber cable or flexible cord of two or more
conductors shall be treated as a single conductor for
calculating percentage conduit fill area. For cables that
have elliptical cross sections, the cross-sectional area
calculation shall be based on using the major diameter
of the ellipse as a circle diameter.
However, it depends on where the conduit is. If the conduit is underground (or any other damp or wet location), then NM cable is not allowed.
National Electrical Code 2011
ARTICLE 300 Wiring Methods
I. General Requirements
300.5 Underground Installations.
(B) Wet Locations. The interior of enclosures or raceways installed underground shall be considered to be a wet location. Insulated conductors and cables installed in these enclosures or raceways in underground installations shall be listed for use in wet locations and shall comply with 310.10(C). Any connections or splices in an underground installation shall be approved for wet locations.
300.9 Raceways in Wet Locations Above Grade. Where raceways are installed in wet locations above grade, the interior of these raceways shall be considered to be a wet location. Insulated conductors and cables installed in raceways in wet locations above grade shall comply with 310.10(C).
ARTICLE 334 Nonmetallic-Sheathed Cable: Types NM, NMC, and NMS
II. Installation
334.12 Uses Not Permitted.
(B) Types NM and NMS. Types NM and NMS cables shall not be used under the following conditions or in the following locations:
(4) In wet or damp locations
Box Fill
Box fill might be an issue. There are 8 current carrying conductors, if they are 14 AWG, that's 16 cubic inches (18 if 12 AWG). Plus another 4 cubic inches for the receptacle (4.5 for #12). And another 2 cubic inches, if there are grounds (2.25 for #12).
Equipment Ground
If there aren't any grounding conductors, you'll either have to install a 2 prong receptacle or a GFCI receptacle with a "No Equipment Ground" label.
What's What
You'll also have to figure out where all the wires are coming from, and where they are going. You can't just tap circuits all Willy Nilly, you have know what else is on them.
Which Neutral
As for which neutral to use, you should defiantly use the grounded (neutral) conductor from the same circuit as the ungrounded (hot) conductor you're using. You could end up overloading a neutral, or other problems if the circuits are out of phase.
Best Answer
I would buy a high grade exterior caulk and caulk the box after you've screwed it in. That should prevent any water or insect intrusion.
As for the connection in the box, a standard NM clamp should do. Conduit is more or less for exposed wire and this wire would be solely inside the wall. Be sure to run conduit or UF cable from the box to whatever you're connecting to outside.