"Chopped" This Drink -- strawberry basil vodka tonic
I doubt there is any combination of these ingredients that I would prefer to a well-made Gin and Tonic.
Why these ingredients? They aren't very inspiring.
Strawberry - A simple fruit that does not lend itself to interesting cocktails. The Gunshop Fizz, for example, relies on other strong ingredients to make the strawberry interesting.
Basil. Seldom used. Strong savory flavor. Easily dominates a drink. Probably best used in a basil version of something like a Mojito.
Vodka. Flavorless in a cocktail, and therefore uninteresting.
Tonic water. Great mixer (if you use a good brand), but not much inspiration by itself.
Looking at those ingredients, it sounds like you're looking to make the sort of semi-sweet refreshing drink that folks in New York drink out of mason jars at the trendy dressed-down brunch places that I can't afford to eat at.
...wait, what was I talking about? Oh, right. I mean, I think with those ingredients, the sort of drink you're going for is kind of self-explanatory--the sort of thing where you'd muddle maybe six chopped strawberries with a couple of basil leaves with one and a half or two ounces of vodka, shake that with ice, dump the whole thing in a mason jar and then top that off with two or three ounces of tonic water.
If I were making something like that I might also add three quarter ounces of lemon juice, and then possibly sugar, the amount depending on how sweet the strawberries are. I might also try playing around with different base spirits than vodka--tequila, for example--to see if there's anything that might add something a bit more to the drink and pull it all together.
If I wanted to go crazy maybe I'd try making a strawberry basil syrup, and going syrup + lemon juice + vodka/whatever + soda water, with amounts varying based on how sweet the syrup is.
But overall, I think what you're working with, in combination, is limited and straightforward enough that you can probably find your favorite iteration of the drink you're looking to make by experimenting until you find what you like best. Other than overdoing it on basil, as Dan mentioned, it's not the sort of thing where you're likely to accidentally make something you'll find undrinkable, so that's probably the best approach.
The tonic is what is throwing me. Can you live without that? Maybe replace with seltzer?
Personally I would make strawberry basil lemonade and serve over ice with the vodka.
You could even serve the lemonade in a punch bowl and make a decorative floating lemonade ice ring. Just fill a bundt pant a 1/4 of way with lemonade, sliced berries and basil leaves and freeze solid. Add another layer of lemonade, sliced strawberries and basil leaves and freeze again. Repeat until bundt pant is full. Keep frozen until ready to serve. Fill punch bowl with the lemonade and vodka and add ice ring. It wont dilute the punch and will look very pretty.