The Shuttles the Asgardians use are one of the few items they themselves developed, or rather, which' design was brought from earth and then refined.
When the ancient tigers built the moonbases, they used heavy lifters using the Orion drive principle ( http://en.wikipedia.org/wiki/Projec....._propulsion%29 ) to ferry the vast amounts of heavy machinery to kickstart Central Control from the planet to the moon.
Every lifting from the planetary surface was done this way from a spaceport built on the frozen ice of the southern polar continent.

The personnel capacities of the Asgardians left little space for such large machines, plus they're lacking flexibility - and if captured by the Reich, would have posed a serious danger to the habitats, due to the amount of troops they could carry.

The answer was the need for a small, limited cargo capacity, but agile, flexible shuttle.
Utilizing the available materials and manufacturing technology, the Asgardians utilized one of the blueprints they had daftly copied before leaving earth when they sponged up whatever they could acquire.
The original device was the Silbervogel :
http://www.luft46.com/misc/sanger.html
http://hemportalen.fi/juhwestm/space/sang-e.html

The Silbervogel-clones the Asgardians build use a rocket engine like SpaceShip One ( http://en.wikipedia.org/wiki/SpaceShipOne ) and it's follow-up's ,
They use NOx as oxidizer and rubber-resine compound enriched with metal powders in the form of "sticks" as solid fuel:
http://en.wikipedia.org/wiki/Hybrid_rocket

Combined with the lighter weight thanks to massive use of Titan and high-temperature-stable alloys, and many weight-saving technologies, and the higher energetic density of the hybrid drive system compared to the liquid fuel drive of the original,

Asgard shuttles are single stage to orbit vehicles. In the lower athmosphere their rockets breathe air and only when the athmospheric density becomes so low as to impair drive efficency the NOx is injected. That way there is a reduced amount of oxidizer needed which also saves on the shuttles weight.
With a load capacity of about 4 metric tons they can carry less than the Space Shuttle, but with their large landing gear they can land and take off even from meadows or deserts if needed, and they need no auxiliary fueltank or booster rockets.
Still, they can take off only once and reach escape velocity, having to drift to the moonbases or rather the Fenris Spacedock thereafter, making each route take between 2 days ( optimum ) up to a week ( worst case scenario ) Shuttles are equipped to keep up to 10 people alive for 2 weeks ( 4 canine crew + 6 humans - 5 humans being the normal size of a Reich's scouting party ).
For emergencies there is sufficient Hiberzine on board to knock out everybody, buying up to a month of additional time for another shuttle, a ferry or a drone to resupply it or take the shuttle into tow in order to rescue it.

Advanced designs configure the two smaller, outer drives as scramjets ( http://en.wikipedia.org/wiki/Scramjet ). As these drives don't operate without air, and likewise not without an already intense airstream, the central rocket is used to accelerate the shuttle to the speed neccessary to trigger the smaller scramjets.
These then provide the thrust needed to get the shuttle to orbital escape velocity.
The higher efficiency this offers again permit shuttles of that generation to actually engage in short hops on the planet before taking off again, or permit at least partially powered interplanetary flight, which means the travel time is vastly shorter between Midgard and Asgard.

The drawback is that those shuttles can only be used on planets with an athmosphere capable to serve as oxidizer as well as requiring a more airplane-like launch profile, meaning the shuttle needs more time to get to speed, yet upon reaching the same height and speed, consumed a lot less fuel.

A ferry usually carries two shuttles along it's spine, ferries patrolling as safety monitors near the asteroid fields usually carry up to 4 shuttles, though two of them are "worker" types with sets of manipulators.

City class vessels likewise carry shuttles along, normally three of which one is a heavily shielded worker type to execute repairs on the drive system when it's still highly radioactive. Although, as the simulations of Central Command's computers insist, the drive pulse bombs are very "clean".