Do the mosquitoes come from any particular source, or are there permanent water features near your home that you cannot control? Has the year been unusually wet? Has your local city run out of vector control funds?

Introducing predator insects can have some effect, but one isolated effort (yours) usually results in most of the predators leaving the yard. If every third neighbor did this, the results would be more noticeable.

Dragonflies come to mind as a mosquito control, but it is hard to maintain a flock of those!

I don't think any of those predators except maybe the biggest of the mantids can take down a Japanese beetle.

Draining larval habitats for mosquitoes is your best bet, but many people do insist that attracting hummingbirds (or bats) makes a noticeable dent in the skeeter population.

A lot of aquatic insects feed on skeeter larvae (including a few species of other skeeter larvae) but I guess they don't really control them, at least not enough for our comfort...

A bat house may be worth a try, if you have seen bats in your neighborhood.