Shove the urchins costumes in a wahing machine with a few tea bags or let them soak [steep] in a bucket of tea/coffee.

Unless you're in a small theatre, often tea staining and coffee staining won't read from a distance - they also tend to stain evenly, which just changes the color.

If you take screening (like from a screen door), and lightly spray paint over parts of the clothes in  various colors, it will give a dirty and stained look. You can also shred dark pieces of netting and apply it over portions of the costumes to give them a raggy look without actually ripping up the costumes.

The sandpaper idea above is really effective - but be careful - sanding fabrics - especially natural (cotton, linen, etc.) fabrics - will deteriorate them quickly, so do it lightly.

I would also suggest making your clothes for the urchins out of heavier fabrics (even though they'll hate it LOL) - tweeds, gabardines, etc. Lightweight fabrics will never give you the look you're going for, as thin, delicate fabrics were a luxury then, and the gang wouldn't have had anything like that.

Good luck!

I agree with tristanrobin. Judicious application of spray paint (black, grey or brown) will quickly dirty up most costumes. Pay special attention to the knees, elbows, cuffs and collars -- anywhere dirt would naturally accumulate.

Best thing I have found to give hems a realistic frayed look is a rotary drill with a wire wheel attachment.  This wears out the fabric quickly and does not leave shrp edges like cutting it with a blade.  This can be done at knees or hemms anywhere you need to strees the clothing.  Be careful when doing this.

I like the standing belt sander for putting wear on clothes in a hurry- but I have to say I filed down my nails in a hurry.  Use only if you don't mind holes in your stuff too.. .