I tried talking with J about the stranger thing and ran up against the same problem in that we do talk to strangers. I have talked to her about if someone tries to take her away that she should yell out "This is NOT my mommy!" or "This is NOT my daddy!" I asked her to repeat what she should say and she yelled out "This is not my mommy OR my daddy!!!" 
I like some of the ways you all are addressing it and will save them to refer to as we are getting to the point where she will start understanding it.
My favorite brussels sprouts recipe is fiddly but so good: separate the leaves of the brussels sprouts (or sometimes I slice them very thin across the grain so I get longer ribbons, but it really is better with the whole leaves). Rinse and saute in a frying pan with a little olive oil until bright green. Toss is some unsalted roasted pistachio nuts, a little salt and pepper and squeeze some lemon or lime juice over top. It makes for a really fresh, bright and crunchy dish - very satisfying. And it doesn't get that taste I can only describe as "olive green" that you get when you boil or steam them whole.
And yes, APA has been getting stuck for me for the past few days.
"Any idiot can face a crisis; it is this day-to-day living that wears you out." -Anton Chekhov