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It sounds like the neutral connection from the subpanel in the house back to the meter base has developed a high resistance. This is a dangerous condition and needs to be fixed ASAP. Power to the meter comes from a center tapped transformer. There are two 125 volt legs of opposite phase sharing a common neutral (the center tap). If the neutral feed to the house develops a high resitance, then the resulting voltage drop in the neutral wire will show as a low voltage (phase to neutral) on the more heavily loaded phase, and a high voltage (opposite phase to neutral) on the more lightly loaded phase -- since the neutral voltage will shift in the direction of the more loaded phase (away from the unloaded phase). If the loads on each phase are perfectly balanced then the neutral currents will cancel out, and both voltages will be the same, even if the neutral has a high resistance. The neutral acts to carry the unbalanced current, or fails to do so, as seems likely in your case. One real danger comes in the fact that one phase can eventually see a very high phase-to-neutral voltage, as much as the full 250 volts. Imagine what this does to items plugged into that phase.
Lights that momentarily get really, really bright is a classic symtom of this condition. Another danger is a function of how the equipment bonding/grounding was done. If the neutral is bonded to the metal box, and the ground rod quality is marginal, then your supposedly grounded metal boxes are ELECTRICALLY LIVE. The fact that the feed cable was spliced is entirely consistent with this -- and the likely cause. Get it fixed right away!!
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