I'll break it down:

I would have to ask the Judge WHOM might satisfy the 'standing' question

"I" is the subject.  "the Judge" is the indirect object.  Here's where the sentence gets interesting: "WHOM might satisfy the 'standing' question" is your direct object phrase, and normally when a who/whom pronoun is the direct object, the correct version is "whom"; however, "whom" is not the direct object here.  The entire phrase is the direct object, and when the pronoun is the subject of the phrase, the proper form is "who".

So let's break down that phrase:

"who" is the subject.  "satisfy" is the verb.  "might" is the adverb.  "question" is the direct object.  "the" is an article for "question", and "standing" is an adjective describing question.