1) The circuitry in the external charger should have, in theory, protected the batteries from any voltage spike that could have occured once the charger was plugged in. Initial power up of the charger or when a battery is put into slot the programming should only send a minimal voltage signal to the battery slot to test charge level of the battery and to determine the battery type before it ramps up the signal, this generally takes 1/2 a minute to a full minute, at least on my Xtar, Nitecore, and Efest brand chargers I have.
2) Though caution would be advised, I'd check the batteries with a Digital Multi-Meter, if you get a voltage reading there is probably no noticeable internal damage to the battery. A voltage spike to the battery, if there was very significant damage the battery would have swelled, outgased (hissed), and electrolyte would have leaked out, if not worse spewed like a roman candle going off. If the battery has a charge between 2.5v minimum to 4.2v maximum, the battery should be fine, though taking it gentle and don't stress them to far for a couple of days would be highly advised to see if they are still staying stable.
Though, caution again, the batteries sound fine from what you have described, just the charger circuit board, most likely the AC to DC converter fried and is what you smelled, but if you are wanting to be as cautious as possible, taking the safe route, take the batteries to a recycling drop off at like Best Buy or Home Depot if in the US and replace the batteries is always a good option.