You cannot cover any junction box that still has live wires in it. Your best bet is to either remove the box all together or just put a cover plate on it. Your other option is to run a new circuit to the new box and de-energize the circuit to the old box and mark the source wires as "NOT IN USE" at your panel in which case I believe you could cover it over.

If there are live wires in the box, sooner or later you will need to get to the box again, which you can't do if you've covered it over! You'll thank yourself later (as will any future home owner).

You're going to want to use a junction box to switch between nonmetallic sheathed cable, and individual wires.

Conduit body must be marked with volume

The first problem you'll run into while making splices in the conduit body (which isn't likely a problem, since most fittings are labeled), is that you'll have to make sure the conduit body is "durably and legibly marked by the manufacturer with their volume".

National Electrical Code 2014

Chapter 3 Wiring Methods and Materials

Article 314 Outlet, Device, Pull, and Junction Boxes; Conduit Bodies; Fittings; and Handhole Enclosures

314.16 Number of Conductors in Outlet, Device, and Junction Boxes, and Conduit Bodies.

(C) Conduit Bodies.

(2) With Splices, Taps, or Devices. Only those conduit bodies that are durably and legibly marked by the manufacturer with their volume shall be permitted to contain splices, taps, or devices. The maximum number of conductors shall be calculated in accordance with 314.16(B). Conduit bodies shall be supported in a rigid and secure manner.

Cable must be secured to conduit body

The next problem, is that the cable must be secured to the conduit body.

314.17 Conductors Entering Boxes, Conduit Bodies, or Fittings. Conductors entering boxes, conduit bodies, or fittings shall be protected from abrasion and shall comply with 314.17(A) through (D).

B) Metal Boxes and Conduit Bodies. Where metal boxes or conduit bodies are installed with messenger-supported wiring, open wiring on insulators, or concealed knob-andtube wiring, conductors shall enter through insulating bushings or, in dry locations, through flexible tubing extending from the last insulating support to not less than 6 mm (1/4 in.) inside the box and beyond any cable clamps. Except as provided in 300.15(C), the wiring shall be firmly secured to the box or conduit body. Where raceway or cable is installed with metal boxes or conduit bodies, the raceway or cable shall be secured to such boxes and conduit bodies.

(C) Nonmetallic Boxes and Conduit Bodies. Nonmetallic boxes and conduit bodies shall be suitable for the lowest temperature-rated conductor entering the box. Where nonmetallic boxes and conduit bodies are used with messengersupported wiring, open wiring on insulators, or concealed knob-and-tube wiring, the conductors shall enter the box through individual holes. Where flexible tubing is used to enclose the conductors, the tubing shall extend from the last insulating support to not less than 6 mm (1/4 in.) inside the box and beyond any cable clamp. Where nonmetallicsheathed cable or multiconductor Type UF cable is used, the sheath shall extend not less than 6 mm (1/4 in.) inside the box and beyond any cable clamp. In all instances, all permitted wiring methods shall be secured to the boxes.

Wet locations

If the conduit body is outside, the AHJ could consider it a wet location. In this case, you wouldn't be able to have NM cable in the conduit body since it's not allowed in wet locations.

tl;dr

In most cases, you'll install conduit off the back of a Type LB conduit body, through the wall, and connect it to a junction box inside the building. You'll make your splices in this box, not in the conduit body.