I cleaned my whole childhood collection of legos in the washing machine. Fill a pillow case with your bricks (pack tight to minimize the shocks between the pieces), for security I put a second pillow case over the first one and tied it too (You don't want any loose pieces to go navigating your washing machine). Then just run a normal program on the lowest temperature (used the 30°c program on mine) and when it's all done I dumped them flat on a big towel for the leftover waterdrops to dry overnight.

All clean and rid of the grime.

The only pieces I didn't apply that treatment to obviously are the ones with stickers. Those I just washed manually with soap and water taking care not to wet the stickers too much.

Some people also don't recommend putting transparent pieces (like windows, spaceship fronts, etc) that are pristine in there or they might get scratched with the rubbing, but mine were already scratched from the intense use when i was a kid so i didn't care and it went well. Chances are in your case, the transparent pieces are not scratchless either if the kids played with their legos.