I remember a trick from How Clean Is Your House and it's now the first thing I try. Put a little bit of WD40 or 3-in-1 oil onto the sticky residue and rub it in with a dry cloth (an old duster or something). The oil will dissolve the glue, just wash in washing up liquid afterwards to clean off any leftover oil. Obviously, this only works on non-porous things, but Lego will be fine.
Hotter water should help soften the adhesives up to the point where it is easier to remove them so I would use a combination of some wahsing up gloves, water as hot as you can manage to put your gloved hand into to pick out a piece and using a scraper or blunt knife remove the sticker and any excess residue and put it back in the water, preferrably in a separate bowl.
then i would pick the piece out oncei it has time to warm up again and scrub it with a nail brush (or old toothbrush) using white vinegar and soap to remove the remains of the glue.
return it to the water to soak and get rid of the vingegar smell before rinsing.
Nail polish remover can also work. But be careful as it can damage some plastics (sort of dissolves them). So if you want to try it, do it on one small piece first. It also smells strongly and you ought to have some ventilation.
Can you handle white spirits? You have to be careful with it, but a tiny bit on a paper towel takes off stickiness from stickers really well, and then just wash the Lego in soapy water to get rid of the residue/smell afterwards. But do be careful and always read the safety instructions, and it does smell very strongly.
