Logistics can be pretty confusing. I am by no means an expert so please correct me if things are incorrect. Info is based on v71 the current paid version as some things have changed from previous versions.
Radius Slider
First off, the radius. The radius is not 100% accurate so be careful when adjusting it if you're trying to exclude some areas. It feels like the radius picks up stuff a little bit beyond what's highlighted. The radius applies to fetch and priority fetch.
Oddjobbers
Oddjobbers who aren't busy will sometimes help out with moving stuff to your warehouses. They do not seem to care about your radius, and a warehouse with 0 workers and fetch/priority fetch disabled will still receive stuff thanks to them. Other workers who are not busy with their job might also help out with carrying.
Fetch
Fetch will have your delivery workers grab what's closest to them inside the radius. They will grab from the floor, import depots, and production storage.
Priority Fetch
Priority fetch will have your delivery workers grab what's closest to them inside the radius, but this will also include non-priority storage, haulers, and unloading stations.
Pull Source
Pull source let's you designate a storage to pull from, and then the icon will change to a triangle. CLICK THE TRIANGLE ICON and you will get a new slider just for that warehouse, along with options to adjust what you want to pull and how much to leave. Pull source ignores your radius slider.
Export Depot (pull source)
The most common use of an export depot is to sell surplus goods from your warehouse. You probably do not want your export depot to grab stuff off the ground before it hits your warehouse. You probably do not want your export depot to grab items hot off the production line before it hits your warehouse. Disable fetch and priority fetch. Use pull source only and adjust the new slider to accurately control how much you want to keep for just that warehouse. Items in an export depot seem to decay faster than haulers, though not as fast as floor decay speed.
Export Depot (fetch)
If you import a lot from taxing other regions, you will find that stuff often overflows your import depots and spills onto your throne. You can set a warehouse to store the overflow (which will overflow eventually) or you can skip that step and set up an export depot nearby with small radius fetch to sweep the throne and sell off the overflow.
Hauler
A hauler is essentially a 1 item warehouse. You place the hauler where you want items delivered. For example, a bread hauler can be placed right next to your food stall. You can have the hauler "fetch" bread out of the baker's oven, or "pull source" from the bread warehouse. Haulers are convenient for moving one item type and take up little space. Items in a hauler have 75% decay compared to 50% for warehouses. Hauler size starts at 80 and can be scaled up to 3520. Hauler workers have the same carry capacity as warehouse delivery workers.
1 Item Warehouse
Just like a hauler, only with better decay rates and potential capacity. Warehouse crates have size 80 but can be upgraded (research not required) to 300, and then 500 per crate. The first upgrade will cost furniture. The second upgrade will cost furniture, cut stone, and pottery. Going from 80>300 is pretty significant, but 300>500 is not for the added maintenance costs. Consider building your warehouses larger so you can hold off on upgrading them.
Multi-item Warehouse
One thing to keep in mind with warehouse delivery workers is that they will grab whatever is closest first. If you have grain and coal in the same warehouse, and your coal source is far away, your delivery workers will only be grabbing the grain nearby during harvest. It is convenient to have lots of items in the same warehouse, but it is bad for items with high throughput.
Janitor Warehouse
A janitor needs a lot of different items but not in huge quantity. A janitor's fetch radius is slightly larger than their servicing radius, but any materials beyond that will not be grabbed by the janitor. It is therefore handy to have a janitor warehouse nearby that contains all the items a janitor will need, and stocked by warehouse delivery workers who can reach across the entire map for stocking. Priority fetch is handy in this case as items are often warehoused like cut stone, pottery, etc. If you do use priority fetch, then make sure your other janitor warehouses are also on priority fetch, else they will be snatched from. If you didn't know, you can click the down arrow next to a warehouse item if you wanted to adjust the size of 1 crate down to 10 or 20 for limited stocking.
Loading/Unloading Station
Loading and unloading stations are used when you need to move a lot of 1 item in batches of 400 and ideally multiple batches a day. They require a lot of workers to maintain good efficiency and will not be very good if understaffed, at which point you might as well use haulers. You build the loading station at the source material and it can only load 1 item type. The unloading station is built at the destination like a market or production facility and can receive multiple different items. An unloading station at the default size can hold 8 deliveries (of 400) and 32 deliveries at max size. Upon building an unloading station, you will need to click on the "Resources" word at the top as clicking on the blank spot beneath it no longer works. Here you can decide how many different 400 item slots you want your unloading station to hold. You could for example build an unloading station next to your food stall, and have multiple different foods shipped to it. Items in an unloading station decay at 50% like a warehouse.
Import Depot Logistics
Finally the most powerful of all logistics. An import depot will receive goods through auto trade, manual trades, shipments from taxed cities, or caravans of loot from battles/conquest. Import depots have 2.4k capacity up to 22.8k capacity. Items in an import depot decay at 75%. When goods are imported, a red hat courier will spawn at one of the road entrances on the map and head to the nearest import depot of that good. They will then unload their goods. If the import depot is full, they will move to the next import depot for that good, and so on until all import depots are full. If they still have items left to deliver then the excess will be dumped on the throne.
As taxed crops are delivered in bulk once a year, you can position 2.4k capacity import depots near your primary food stall gathering areas to receive them. A large shipment of 10k mushrooms can fill to capacity 4 of the 2.4k import depots with the extras spilling onto the throne. Free delivery without needing a single logistic worker or warehouse if you just leave the mushrooms in the import depot for grabbing. As for taxed items that are delivered daily like coal, you can import more than what you use, and gradually fill up multiple coal import depots scattered around your city. After a while, you will have a coal import depot filled to the brim by your smelters/smithies, your bakers, your brewers, and all of your bath houses. No logistic workers or warehouses required to store the coal. A giant shipment of 20k grain can be placed in a large import depot right next to your bakers, who no longer need to be near grain fields or a grain warehouse. 0 workers required to carry the grain across your fields because it is all delivered to giant import depots. I also like putting import depots near my army supply storage to receive the spoils of war, or when I an unequipping my armies.
Carry Capacity
On v71 the base carry capacity for warehouse workers and haulers is 10. Food stall workers, other workers who have free time, and oddjobbers have carry capacity of 6. The admin research upgrade for carry capacity will increase carry capacity by +1 per level for only warehouse workers and haulers.
