How good is liquefaction?
L.Dutch's answer is the right concept, but his numbers are wrong. 6 liters is the maximum inhalation of an average adult male; however, men have much larger capacity than women and normal respiration does not fully inflate the lungs. The 62 liter volume of an average adult assumes a resting inhalation volume which actually averages closer to 2.5 liters of air in your lungs (during normal at-rest breathing across genders). Volumes of gastro intestinal gases vary a lot throughout the day, but average about 1 liter. This means his equation should look more like 3.5/(62+3.5) = 5%; so, you only get a 5% reduction in absolute volume.
That said, the more important savings are in removing the empty spaces around the body. An average human is 160x39x23cm that is 143.52 liters. When you compare that to the 58.5 liter liquid state of a human, you get 143.52/(143.52+58.5) = 71%; so, your reduction in practical volume would be 71% compared to shoving us in boxes.
This will result in the following:
Age Group | Avg. Whole Weight | Avg. Volume
2yr old Toddler 12,000 g 11,100 cm^3*
13yr old Teenager 45,000 g 41,600 cm^3*
Adult 62,000 g 58,500 cm^3
*Due to lack of data, child volumes are based on mathematical ratios compared to adults.
Different childhood ratios of bone, muscles, organs, etc might impact these figures.
Designing the packaging:
To package your humans this way, place thier remains in large plastic bags kind of like IV bags. This will keep your remains separate, sterile, and waste very little space.
That said, because some fluids such as stomach acid would react with other fluids such as brain chunks, you may in fact want to store certain biological substances separately rather than in on big bag to make sure you still have all the same compounds coming out as you had going in. This may mean a complex system of "disassembling" the human body into seperate bags rather than just throwing them into a blender. This can lead to some unexpected wasted space as you start needing to account lots of total bag materials, air gaps between bags, and possibly wasted space in whatever bins you use to keep all the liquid human sacs organized in. It's hard to say just how much space will be wasted without delving REALLY deep into human biochemistry and industrial design to determine how many bags and of what size you need; so, lets just say it will still be more efficient than boxing whole humans, but maybe closer to a 50-60% savings if you go this rought.
But, your aliens could do better
Generally I agree with Carl's assessment that you don't need to bring whole people, but cloning humans requires large artificial wombs, and lot of labor for your aliens to hang around baby sitting us for 20 years waiting for us to have a functional adult population while our DNA synthesizes all the complex compounds (proteins, fats, nucleic acids, carbohydrates, etc.) that make up an adult.
Instead of a slurry which is 60% water, you could dehydrate the human pulp into a "meat and bone meal". This is an industrial term referring to the dehydrated and ground up remains of an animal. Since any planet they are bringing us to would inevitably contain lots of water, they would just need to rehydrate our remains as part of the reconstitution process using the water from our new world. https://en.wikipedia.org/wiki/Meat_and_bone_meal says that meat and bone meal averages 4–7% water (I will use 5% to simplify the math); so, if you reduce the human body from 60% water to 5%, you are eliminating about 55% of a human's total mass.
According to calcert.com, loose meat and bone meal is has a density of 0.72 g/cm^3. This is a bit less than our liquid density because the powder will have room for air, but will still have a lower total volume than liquid humans while allowing the aliens to transport all of our complex compounds needed to put us back together.
This will result in the following:
Age Group | Avg. Whole Weight | Avg. Dry Weight | Avg. Volume
2yr old Toddler 12,000 g 5,400 g 7,500 cm^3*
13yr old Teenager 45,000 g 22,250 g 30,902 cm^3*
Adult 62,000 g 27,900 g 38,750 cm^3*
*Due to lack of data, meat and bone meal density is based on animal meal. Human meal
might be slightly more or less dense.
If the remains are vacuum sealed like coffee, you could increase the density of your meal to be just a bit over 1 g/cm^3; however, vacuums cause most organic compounds to break down; so, depending on how advanced your alien tech is will determine how much they can safely compress your human remains.
Going back to the practical volume of a human, this means you will get somewhere between a 79 and 84% practical reduction in volume by converting people to meat and bone meal. That is about 34-53% more efficient than liquefaction (ignoring any differences in packaging processes). If you opt for liquefaction in your story, I would suggest giving some brief handwave explanation for why you can not dehydrate the human remains.
Designing the packaging:
Another possible advantage to removing water from the human body is that it makes freezing us far less destructive. Water expands when freezing which plays havoc on on the other molecules being frozen with it. The Arrhenius equation shows that as things cool, things that react at higher temperatures stop reacting with one another. This means you can deep freeze stomach acid and dehydrated brain chunks together without them reacting with one another such that you can get an even better efficiency out of your packaging by keeping us in one very cold container.
Even under low-vacuum states, vacuum sealed plastic and foil cubes are probably the best way to store and separate human remains because they maintain a sterile, light weight, easily stored, separate vessel for each human, and can be shaped into cubes for optimal space efficiency. To figure out how big these cubes have to be we should look at the top end of who the aliens might select for transport. If they want to save the species, they will probably select people based on health factors meaning the obese and dangerously tall may be excluded. This puts a reasonable upper limit of 115kg on your whole weight. If we assume a light vacuum seal will compress the meal density to about 0.85 g/cm^3, then we get a finished volume of about 60,882cm^3 or a cube that is about 39x39x39cm.
If it were me, I would describe the human storage room as being a cryogenically cooled cargo bay full of pallets of vacuum sealed blocks, all ~39x39cm at the base so that they stack nicely, but ranging from ~4-39cm tall. By mixing and matching people of various volumes, each pallet could be filled to the maximum height recommended by alien freight regulations.
There are many factors that could play into how you could and should store a disintegrated human, and it all boils down to "how destroyed is too destroyed to reassemble." Hopefully this goes into enough (though be it disturbing) detail to figure out how compressed your humans should be.