Does JotForm enable choice elimination?

Over 150 people will use the form, with each person asked to choose an option from a list — first come, first served.

Does JotForm enable dynamic choice elimination so that options already chosen by one user will not appear when another user access the form?

Yes, we have that kind of widget in which options are eliminated or crashed out once it's out of stock. Check this out: http://widgets.jotform.com/widget/gift_registry

If you want users to select multiple quantity, use this: http://widgets.jotform.com/widget/quantity_gift_registry

Hope this helps!