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According to the PHB/basic rules,

Weapons and armor used by monsters are rarely in good enough condition
to sell.

Are nonmagical weapons and armor used by monsters in good enough condition for PCs to equip and use themselves?

As a rule, yes. If it fits

The section you quote is specifically about selling equipment that you find (PHB, p. 144)

Selling Treasure

Arms, Armor, and Other Equipment. As a general rule, undamaged
weapons, armor, and other equipment fetch half their cost when sold in
a market. Weapons and armor used by monsters are rarely in good enough
condition to sell.

Rules for using equipment you find are found other places. Some significant rules are found in the following section on Equipment Sizes (PHB, p. 144, bold added).

Variant: Equipment Sizes

In most campaigns, you can use or wear any equipment that you find
on your adventures, within the bounds of common sense. For example,
a burly half-orc won't fit in a halfling’s leather armor, and a gnome
would be swallowed up in a cloud giant’s elegant robe.

The DM can impose more realism. For example, a suit of plate armor
made for one human might not fit another one without significant
alterations, and a guard’s uniform might be visibly ill-fitting when
an adventurer tries to wear it as a disguise.

So most of the time, if you find equipment and it is reasonable for you to use it, you can. A DM is the final judge of what would be "reasonable" to use. Note that this decision could be based on something other than a creature's size. For example, a bow made for an Illithid could have a grip too alien and strange to be comfortably used by a humanoid. Also, whether or not equipment has been damaged may be a factor. A DM might decide that armor worn by Orks is usable if they were disabled by a sleep spell, but not if they were killed by a might blow from a warhammer. Armor that usually would fit might become too dented to be worn after you kill its occupant (although a DM might then have to bend over backwards to explain why your own armor is wearable after you've succeeded on three death saving throws).

However, some DMs may ignore any of these concerns and declare that every piece of equipment you find can be used by you. It all comes down to what they consider "common sense."

This statement is mostly there to prevent ludicrous amounts of not-very-useful loot being distributed for every goblin or bandit in the game. It's a guideline rather than a rule, what loot is available (and what condition it is in) is ultimately up to the DM, but it's just kind of a waste of time to end up with 23 long swords, 14 short bows and 35 hide armors every time you run through a bandit stronghold.

Arms, Armor, and Other Equipment.

As a general rule, undamaged weapons, armor, and other equipment fetch half their cost when sold in a market. Weapons and armor used by monsters are rarely in good enough condition to sell. (PHB, p. 144)

It'd also increase the gold value of an average humanoids loot quite significantly if all their equipment was PC-grade weapons and armors, although I'm not sure how much of a problem this is in comparison with all the micro management that'd have to happen in this situation.

As cited by other answers: Yes ... but they might not want to:

• fleas and ticks on fur/leather/wooden armor (Diseases)


• rust and broken links on metal armor reducing its AC rating to half


• altered stats: a Rhino-Orcish-Leather might weight 10 extra pounds which the orc can carry easily


• protective shaman paint (gecko-feces mixed with stinkhorn-paste) or other "modifications" like added skulls or teeth-chains of slain foes


• sweat, snot and blood (not to mention grease resulting from bad eating habits) of the former user of it


• slashes / gashes from killing the last owner

It might need serious alterations (already mentioned above):

• 
  Variant: equipment
  sizes

and when brought to a skilled craftswoman they are hesitant to deal with it:

• "I have to charge double for even handling this piece of garbage"


• "If I modify this for you and it breaks, my name is ruined - no way I'll do that"


• "What is that ... substance ... - is it blood? ::faints::"

There are lots of creative ways to dissuade your party from taking all on board - maybe even a (low level) plot:

"Me revenge - you stole mighty armor of Uncle who slaughtered Sabertooth - gimme back or die!"

Another rule to remember... encumbrance. Have the party explain how they will transport all of these items. Even pack animals can only carry so much. If the burly, 20 STR warrior, is towing all the equipment for the party between a couple of poles....what disadvantage does a DM want to impose?

As far as the PC's using equipment? DM discretion is advised. If the party is starting out at 0 or first level and has almost no equipment then an argument can be made to allow. At even slightly higher levels...would you want to change your equipment for those looted off a dead body? DM then needs to decide to see if it will fit, if it needs repair and what would be the time and cost to restore? Again, weight becomes an issue.

Hope these thoughts help you.