What does it take to move an unwilling status afflicted humanoid when they are:
There are many logical answers, but the players handbook provides unwilling movement rules only for grappling.
It sounds to me like you're asking if you should use the grapple movement rules or the encumbrance rules. The grappling rules say you can move someone with you at half your speed when you have them grappled. But you must first succeed on the grapple.
If I were the DM, I'd use grapple rules for prone and restrained enemies since the ability to escape would not be impacted (although restrained enemies have DA on DEX checks).. All the other conditions eliminate the enemies ability to escape completely. Since Escape is an action and the other conditions disallow actions.
In the other conditions where escape is not possible, I'd use the lift/carry rules. The base lift/carry rules only mentions carrying capacity but not specifically other creatures, that amount being 15 times your STR score in lbs. So let's say your STR is 15, your max load would be 225 lbs. You can lift/drag/push up to twice that but any more than that 225lbs and your movement is reduced to 5 ft. Assuming some armor and weapons, a typical human/dragonborn/tiefling/dwarf body would probably push you over this amount. Halfings, gnomes and elves may not.
Having said that, you would get better movement rates by using the grapple rules if you could consistently beat the escape checks, or somehow convince your prisoner not to attempt escape. Essentially, it would be like you're forcing them to walk on their own, rather than dragging their body with you.
In the case of your spider example, I would probably use the Variant Encumbrance rules to model the situation because a little more granularity would be beneficial. In this case, your spider would likely be carrying more than 10x its STR score, which would reduce the spiders MV by 20ft and cause it to have disadvantage on ability checks, attack rolls, and saving throws that use STR, DEX, or CON. Still a scary proposition for the person being dragged, but offering a realistic opportunity for the reduced party to rescue the victim.
By RAW, grabbing someone in any of the listed conditions would still be grappling, and, theoretically, each condition would just have an effect on the creature's ability to avoid and/or escape being grappled and moved. Interestingly enough, none of these conditions can prevent a creature from resisting the grapple. The grapple check is neither an action, a reaction, nor even a saving throw (the things those conditions prevent), and is therefore not excluded, even by being unconscious.
That said, RAI is a whole other can of worms. It's likely that the above conditions, excluding prone and maybe stunned and restrained, are intended to prevent the creature from making opposed checks, or to impose disadvantage.
A bit of sage advice I just found clarifies that this is left ambiguous on purpose, but backs up the general idea that this is how the interaction would work in most cases. If I were DM I would go so far as to use encumbrance rules depending on the scenario.
The rules for lifting and carrying are on p.176 of the PHB. In a nutshell you can lift 15x your strength score and drag 30x.
If your total load is less than your lifting capacity you can pick it up and carry it around. If is greater than that up to your dragging capacity you can push or drag it or lift it over your head but not move with it. If it is heavier than that you can still drag it or carry it but your speed drops to 5 feet.
As an example, a fighter with 18 strength can lift 270 lb. and drag 540 lb. and is probably carrying about 100 lb. of his own gear. This means he can lift a creature and their gear if the combined weight is less than 170lb. and drag them if less than 440 lb. The pathetic wizard with 8 strength with 20 lb. of his own gear can lift 100 lb. or drag 220lb.
PC races weigh between 37 lb. (Halfling/Gnome) and 380 lb. (half-Orc) plus the weight of their gear; anywhere from 20-120 lb. so this is a relevant consideration.
If the thing you want to move is an object (which includes dead but not undead creatures) then that's all you need to worry about.
If the thing you want to move is a creature than things get more complicated.
If the creature is not resisting your attempts to move it around then you are not grappling. For example, carrying an ally out of the combat or if the creature is not in a position to resist; see below.
If you are grappling, then in addition to the weight restriction, your speed is cut in half. If your speed is now less than 5 feet and you use the grid variant, because of how speed is rounded, you can't move and so can't drag or carry your opponent.
As to the specific conditions, by the RAW:
You can decide that some of these RAW as stupid, as indeed they are, and house rule something else.
