Organic Living spaceships do seem absurd at aou current level of Technologybut given some time, say 1,000,000 years, it wont. Its the holy grail of Technology. I mean sometimes the organic vesion of something is superior to the Mechanical version - Ie computers vs the brain/We repair faster (and in some cases better) than a car or building.
Also, Living doesnt necessarily equate alive-(read thinking). I mean The human(/Vasudan/fox/cat/Um...er...Whatever) body is living, but it is the Brain that makes them truly alive. In a sense, the brain is the Pilot in the fighter...
A lot of what follows is my own speculation
I think that Shivan Vessels are like a cross between Terminator (T-800 series Model 101 (The Arnold Skinjob)), the Borg and Xenomorphs from Alien Quadrilogy.
They have basic mechanical endoskeleton includes some corridoors (Remember, we only see one)(Say I was the Transport and where the shivans landed was my left collar bone. Now say that collar bone was held together with a specially grown skin.-Terminator.
The Skin once grown, hardens like a
crusta- (Cant spell it) - Lobster or Crab shell
In the toughest places, this skin-shell is left unarmoured. But in Thinly covered places it is re-enforced with armour. Also, the skin is covered in a variaty other instuments. - The Borg
Interior is a mix of organic and mechanical Tech. Design in mechanical looks like a warped version of normal mechanics on terran ships. Interior design in the organic area is something by Geiger
Wiring and power-conduits are a mix of organic and mechanical. (Nerves connect to cappacitors, Veins/Arteries connect to mechanical piston pumps <- that sort of thing
The skin and endo-skelleton are capable of growing over the course of years (Much like our skin grows). Think of them being abit like Time-lord Regeneration for how the - only they take about a year to complete
The organic hulls are able to heal over time. (This offers an explanation to something in-game...In the mission where you have to destroy the Sathanas' main beam cannons, I managed, without cheats, to get the Sathanas down to 87% hull...In the next mission, High Noon, The Sathanas was back up to 92% hull. The amount of time between the two missions didnt seem long enough to justify a repair crew...so ipostulate organic healing)
The organic parts thrive on either nebula gas, or the energy emitted around subspace nodes...(Hey for all we know, it could be Shivan's Catnip
Growth occurs in major spurts every few hundred years. Ships which have just had a growth spurt or are in the middle between spurts are put into combat duty. The spend years practically unchanged apart from small differences, like weapons and the nerve/wiring configuration
When a ship is about to have a growth spurt or is having one, it is withdrawn from service and kept at a drydock. The armour is removed and refitted after the growth is complete
Cains would grow first grow tougher, developing into Liliths
Liliths grow in size and shape developing into a stop-gap ship, which I shall refer to as a Lilin (Look it up) (note: this ship is one ive created, otherwise the Evolution of a Lilith into Demon Doesn't make a whole lotta sense)
Lilins look like a cross between a Demon and a Lilith. The exact look of a lilin i haven't decided, but imagine a corvette that looks half-way between a Lilith and a Demon, and you'll have some idea of what it would look like - i might do a sketch some time and ask someone to model it.

The Lilin Eventually grows into a Demon.
Demons then grow into another stop-gap I'll call the Archdemon (again ive created this ship for reasons of pure sense)
Archdemons are a half-way between a Demon and a Lucifer.
The handfull of Archdemons that survive long enough then grow into Lucifers
The few Lucifers that survive to old age then become something else - juggernaut that looks Luciferish (Hey, the ravana destroyer looks Sathanasish)
***Cookie to the person who find the pattern in the nomenclature and for those who got my joke earlier in the post***
Something similar happens along the Rakshassa line, culminating in the Sathanas
That is my opinion. You guys are all free to "believe whatever you want to believe"