All splices need to be made in junction boxes. If all the runs were cut off in one place, you could theoretically use one large enclosure for this. It must remain accessible permanently so no burying it in a wall.
Before you proceed, since you said this is a trailer, you must identify if the existing lines are aluminum or copper and proceed accordingly.
Whether or not you can put in overhead service depends on your local jurisdiction.
As far as identifying what runs where, one way is with an electronic circuit tracer that connect to one end of the run and injects a tone on the conductors that the receiver can pick up. Anther way is to make up a plug with hot and neutral shorted and use an ohm meter to find them at the panel side. Note that light switches in the on position will complicate this unless the lamps are out of the fixtures.