I was troubleshooting a home circuit that appears to have 4 double receptacles and one light on it. One of the receptacles works fine as does the light. The other three show 120 vac hot to neutral and hot to ground. Neutral to ground shows 0 ohms. I'm told the three problem receptacles worked for years and then just stopped. I plugged an answereing machine with an led call count indicator into one of the bad receptacles. It would not fully light up but it was barely illuminating in a pulsing fashion at I would guess 2 or 3 cycles/second. I plugged a cell phone charger into it. It would pulse charging/ not charging at about the same rate. The multimeter showed a solid 120 vac. I tried an incandescent light, but it would not illuminate. I did not check the neutral connection at the load center since one receptacle and the light worked fine. I was told there are no GFI's in this circuit despite one receptacle near the kitchen sink (but it is an old house). Any ideas what is causing this?
My guess is that some part of the wiring chain from outlet to outlet is using back stab wiring connections at the outlet. These can develop intermittent faults that will pop in and out of connection depending on how much current is being asked for by the load. In the case of your multimeter it represents almost no load on the circuit and the intermittent connection stays connected and permits the AC voltage to be read. Light loads cause the on/off behavior that you are seeing. A heavier load results in the intermittent opening up until the load is removed.
You will want to inspect the outlets to see if there are indeed back stab wire connections. If so remove them and replace with new quality outlets that use screw terminals or screw clamp connections for the wire.
As always advised when working with electrical fixtures turn off the circuit at the breaker panel (or fuse box if it is really really old). If you are unsure of working with electrical or not at all familiar with it then call in a licensed professional electrician.
Also keep in mind that intermittent electrical connections can be very dangerous and create heat and cause fires so address this problem as soon as possible. Be advised it may be in your best interest to shut off this particular circuit at the panel until it can be properly repaired.