Who would be able to defeat them? God-level entities like Q and the Xeelee obviously could. Galactic scale civilizations like Star Wars probably could do so eventually by weight of numbers, if their weapons were powerful enough (I don't know if turbolasers would have a significant effect, and photon torpedoes would barely scratch them).
Some basic data for those who are unfamiliar:
The planetoid warships of the Imperium are the size of the Earth's moon (Utu-class) or slightly larger (Asgerd-class). They're FTL-capable, but at hundreds of times c, or a few thousand at best. They carry smaller non-FTL-capable warships. They have "gravitonic" missiles, which seem to be very powerful - they're definitely considered much more powerful than the Achuultani multi-gigaton antimatter weapons. (At the end of the series, a sun-destroying bomb is discovered).
Power of weapons:
The Armageddon Inheritance, chapter 16 wrote:Yet before the last Protector perished, he saw one great warship advance upon the Hoof [Iapetus]. Its missiles reached out—sublight missiles that took precise station on the charging moon before they flared to dreadful life. A surge of gravitonic fury raced out from them, even its backlash terrible enough to shake the wounded Earth to her core, triggering earthquakes, waking volcanoes. Yet that was but an echo of their power. Sixteen gravitonic warheads, each hundreds of times more powerful than anything Earth had boasted, flashed into destruction . . . and took the moon Iapetus with them.
One warship can destroy Saturn's moon Iapetus. A single ship also destroys Earth's moon, but apparently by moving it into the sun rather than explosively. Also, the size figure for a Utu-class warship: 3202.795 kilometers in diameter. (The Asgerd ships are somewhat larger; I think about a quarter more massive.)Mutineer's Moon, chapter 3 wrote:
... what happened to the real moon?"
"It was destroyed," his informant said calmly. "With the exception of sufficient of its original material to make up the negligible difference in diameter, it was dropped into your sun.
Speed, warp and sublight:
[quote="The Armageddon Inheritance", chapter ]which limits their [the Achuultani]best supralight speed to forty-eight lights; seven percent of what Dahak can turn out, six percent of what the Guard can turn out under Enchanach Drive, and two percent of what it can turn out in hyper[/quote]
"All ships, open the range," he snapped, and the Imperial Guard darted suddenly astern at sixty-five percent of light-speed.
Damage resistance: It's hard to find a good quote explaining the shields, but they're definitely capable of stopping multi-gigaton weapons (which is the biggest they're subjected to) in large numbers. They can be penetrated by a missile popping out of hyperspace between the shield and the ship, though.
So, a 10 gigaton weapon, even if it isn't blocked by the shield, is a minor injury.The Armageddon Inheritance wrote:Alarms screamed as a ten-thousand-megaton warhead exploded almost on top of Royal Birhat. The huge ship quivered as the furious plasma cloud carved an incandescent chasm twenty kilometers into her armored hull. Air exploded from the dreadful wound, blast doors slammed . . . and Birhat went right on fighting.
"Moderate damage to Quadrant Theta-Two," the sexy contralto said calmly. "Four fatalities. Point zero-four-two percent combat impairment."