I find soaking in soapy water over night and using one of the heavy duty knitted stainless steel pan scrubbers fair rips off the labels .
Any awkward bits found after rinsing off ...use a drop of neat washing up liquid and one of the micro fibre cloths that's been well used & again the knitted wire pan scrubber .. the glue will not adhere to the soapy surface as you loosen it .
Re the vinegar smell.. vinegar ....being acetic acid ought to be neutralized by an alkali so have a look and see what you have in the cupboards .
Sodium bi carb

Unscented chlorine bleach . Ammonia ?
It could be worth a punt making a solution up and soaking the seals/ lids for a wee while in it and then rinsing them off in rather hot water .
Same with the jars , some jars still carry the vinegar taint even after they have been through the dishwasher on the hot cycle.
Brand new lids on their own for various euro standard size jars tops are available on line .. just can't remember where at present .