If you are reasonably sure that there is no forgotten outlet or other device in this circuit on the first floor above the sound of arcing and sparking, then it sounds like you'll need to open up one or more inspection holes in the ceiling.
Considering that this may be the result of a lightning strike, it could involve more than one circuit, only one of which is now tripping a breaker, so it's not something to delay addressing.

I am 99% certain that there are no other devices on the circuit, as I went all around the house with a tester. I was figuring that we'd have to open up the ceiling, fixing of which will be more expensive than the electrical work. The ceiling boxes are all very tight with the drywall, and the joists are perpendicular to the unfinished area, so there's no room for poking around, though it might be possible to open a hole that's covered by the surface fixture and peek around. But this seems like something for a professional who has the right tools and experience.

You can check inside the fixtures, and at junction boxes you have access to.

these are often common places for failures to occur.

An actual failure in the branch circuit cables is not as common, but if there is a weak spot in old insulation even a nearby lightning strike can produce enough further damage to trip a breaker (and ruin a section of cable by producing a permanently damaged spot in the insulation).

We used to use 'meggers' (mega volt meters) to produce high voltage to trouble shoot these types of problems, but most modern digital meters in resistance mode on a turned off and disconnected circuit are more than adequate for checking insulation for weak spot.

This post was edited by brickeyee on Fri, Jun 14, 13 at 16:34

It might be easier to re do the circuit than to fix the old one. You might try to figure out what order the outlets and lights are in. For the lights, remember that the main circuit can go to the boxes with loops to the lights or can run to the lights with loops for the switches. If you are lucky, you might find that the problem is right before the last device in the circuit and you can get along without it.

I'd look first where the sizzleing, popping and fumes are coming from. By opening up the known junction boxes, you should be able to visually detect if the fault is there.
An inspection hole can be covered, at least temporarily, by a prefab plastic access panel that can be found at a builders supply store (or electrical supply or plumber's supply).

"I was figuring that we'd have to open up the ceiling, fixing of which will be more expensive than the electrical work."

Wow! You either have a very expensive finisher/painter or a very cheap electrician. I have had customers say, "Run a new circuit, I don't want to have to patch a hole." Ok, If I am $100+ per hour. How expensive is their painter?

Thanks, all. I will take home a meter and measure resistance. I disconnected one of the two fixtures and the breaker still tripped. I can easily disconnect the other and the outlets and do the same. Unfortunately, we do need both the outlets and the lights, so there is no shortcut here.

The is one of those things tat hiring someone fr is painful expensive, but if you can DIY can save a lot of money.

One 'trick' to checking permanent wiring to use an extension cord to 'stretch' meter leads.

You can plug the cord into a receptacle ad then measure the resistance at the far end between another junction with the permanent wring included.

It ranks up there with using an extension cord to make a ground available for voltage measurements on 'hot' circuits in older work with no wired ground.

Our electrician called to check on the issue, and he thought the most likely explanation is a bad breaker. He suggested that 1) I disconnect the wire from the breaker and measure resistance of the circuit. (He knows me well and that I have an EE degree). If it's low, then there is a short, Extension cord is a good idea, though the outlets are readily accessible. If resistance is OK, he suggested that I then swap breakers with another circuit of the same rating. If the old breaker trips, it's the breaker, while if the new breaker trips, it's the circuit. Fortunately, these circuits are not essential for our daily life, so I can take my time.

For situations such as the one you describe, I use a pigtail socket with an incandescent lamp, 15 watt is smaller and not as easily broken as is the 60. Remove the circuit conductor from the breaker, place one of the pigtail leads to the breaker and wire nut the other to the circuit conductor. Thus the incandescent lamp is now in series with the circuit. So long as there is a load or short circuit, the lamp will be lighted. When the problem is located (working it hot) the lamp will go off. This allows testing with very low current, limiting potential damage to any conductors. But remember that the circuit is energized and as potentially lethal as any other circuit on the premises.

Thanks to all. This morning, 5 days after the breaker tripped, I disconnected the circuit from the breaker and it did not trip. I then put in the pigtail, turned on the breaker, and the bulb did not glow. I put a bulb in one of the fixtures and turned it on, and both bulbs glowed. I then reconnected the circuit and all outlets and lights are working.

My diagnosis is that something got wet and shorted, and now dried out. If so, this will happen again in the future. Is there another potential explanation? Should I replace the circuit wiring anyway (at least at the panel, it's BX)?

That is actually a very possible scenario with older AC cable with cloth covered rubber insulation.

Find the wource of the water.

Water in walls a ceilings enough to soak into older AC cable is going to do a LOT of other damage if not stopped.

The wet cable will be the least of your problems if you have a water issue (and yes, just replace it with a section of NM).

This post was edited by brickeyee on Sun, Jun 16, 13 at 15:51