I am trying to figure out how many drinks to serve.

Around 10 of the guests are children. For the adults, about 40% are fairly heavy drinkers, 50% are light to moderate drinkers.

We are renting a slushie machine and plan on 6 gallons each of strawberry daquiris and frozen lemonade (bartender will add alcohol for those who want). In addition, we plan on 2 or 3 kegs, with a few cases of light beer. We may also serve a wine spritzer or some type of punch (how much?).

We will also be serving (3 gallons each?) of sweet and unsweetended tea; a mixture of sodas (perhaps 10 cases?); and 10 cases of bottled water.

First a caution; as discussed on the beverage planning page, in many states the host is legally liable if a a guest has a DWI accident on the way home from a party or event, even with private parties. What that means is, you should stop serving alcohol at least an hour before the end of the party (maybe when you serve the snack?) and have a coffee service then, dinner coffee service level if you look at my beverage planning page. Protect yourself and your guests.

Your light drinkers will drink 3-4 drinks, so 45x4=180. Your heavy drinkers, 6-7, so 7x45=315. Total, around 495, max.

You have 96+ drinks of each slushie, around 200 total. 3 full kegs at 160 bottles per keg is 480. 48-72 light beer. Total, around 750. I would suggest, too much... 3 pony kegs (1/2 kegs) for a total 240 would be my first suggestion. Wine spritzer is completely unnecessary.