Why do you bait me so? (

)
Historically speaking, I used to reckon the Dilgar were horribly overpowered. I have now changed my mind on that one- the early EA are pretty vicious as well.
They have two separate families of ship, one of which does speed 4 to 5, and one of which does speed 10 to 16 (Bax's Rishekur.) Your very largest ships are hybrids, speed 7-8.
To avoid being lynched, trot the assault ships out from time to time. To eat planets, use the strike cruiser family.
The Dilgar possess vast quantities of short to medium range firepower. Mount this on large numbers of fast, agile, medium- small ships and tactics become pretty obvious- wolfpack.
Even if it doesn't work, furballs are always fun. Rush them, but do it intelligently, look for a weak spot to pour through or make one with torpedoes, choose whether to hazard small ships that you can afford to lose or medium ships which can take the punishment.
Don't be afraid to take on much larger ships. Think of the strike cruisers as glass jawed swordsmen facing heavyweight boxers; your weapons are much more lethal- but his are enough to do for you if given the chance. Don't give that chance away.
I referred to the Omelos class as 'Satan's Spanners' once- good luck unbolting your oppnents.