As noted above, you can dethatch as soon as your lawn dries out from this rainy spell. To cut down on mulch in the future, make sure that your lawn mower has a true mulching blade on it. A mulching blade will cut the grass into finer pieces, reducing the need to dethatch as often, and those smaller pieces will return nutrients into the ground acting as another fertilizer.
I usually put down fertilizer once I see significant growth. I like Milorganite since it’s much cheaper than Scotts, is organic and won’t burn the lawn, and you don’t have to worry so much about spread rate. This has helped turn my lawn around. Note that Milorganite does not include weed control.
I would use pre-emergent weed control soon. It may be too late in some spots like next to a curb or road where the ground has heated up faster. I also like to use a weed control liquid and spot spray with a can sprayer rather than an full granual product application. But spot spraying may not be feasible is you have a large property.
It’s beneficial if you have your lawn aerated prior to overseeding. It’s best to do in the Fall with the cooler temps, however, you can do it in the Spring as well. Just know that you’re going to have to water all of that seed everyday for a while and then regularly thereafter once it germinates. Using a starter fertilizer or Milorganite with the new seed is a good idea.
For a nice kick before your party, you can fertilize maybe a week or two prior and your lawn will have a deeper color. You can also spray liquid iron for a deeper green. Finally, mow high as it’s healthier for the lawn and prevents sunlight from reaching weeds.