The typical answer would be to get rid of the blackbirds somehow or get rid of the grubs. The grubs in the lawn may be the larva of several species such as June beetles or Japanese beetles. Since grubs may stay in the ground for several years, the number of grubs (and so the number of blackbirds) may fluctuate from year to year. You can easily monitor the number of grubs present by lifting a section of turf. A few (two to three) grubs should not raise an alarm, but if grub numbers are greater than eight or so per square foot, some type of control may be warranted.
Contact your local Cooperative Extension office for more detailed information on grub control in turf.
To control blackbirds, visit the link below.
Online Resources:
Blackbird Control