Do your characters say, "I'd like to buy that Long Sword +1," or is that "+1" for OOC reference only?
Whichever you prefer.
Typically when discussing items after they have been identified the enhancement bonus of a weapon is completely dependent on whether or not your group would find mentioning the numbers to be atmosphere-breaking and unwanted.
If you're speaking to a character after they have found and identified a weapon they'll need to know the level of enhancement and special characteristics of the weapon so they know what bonus to give themselves when attacking various critters, however when you're trying to describe things in game and find mentioning numbers would break the atmosphere, I recommend getting a little flowery with your descriptions.
You can use the following descriptors to flower up your text:
- Masterwork Weapon: This weapon is perfectly balanced and has been crafted by a master weaponsmith to improve its ease of use when fighting evil creatures
- Masterwork Armor: This armor has been crafted by a master armorsmith, and the seams of the armor do not impede movement as much as a normal set of armor would.
- +1: This weapon has a slight enhancement to improve its effectiveness against enemies of any kind.
- +2: Substitute "moderate" for "slight"
- +3: Substitute "substantial" for "slight", the weapon quivers slightly, indicating its power when held.
- +4: Substitute "strong" for "slight", the weapon hums lightly in your hand and fills you with a sense of strength.
- +5: Substitute "overpowering" for "slight", the weapon resonates powerfully in your hand, filling you with power. You feel that this weapon has been enchanted by a master wizard and has an edge stronger than most you'll find, and easily cuts through almost anything.
- Keen: This weapon is sharp, overwhelmingly so, and easily pierces armor.
- Flaming: This weapon fills you with warmth when picked up.
- Frost: An unearthly chill cascades through your body when this weapon is picked up.
- Shock: Your hair stands on end when removing this weapon from its sheath.
- Adamantine: This weapon has a green hue, and a sharp perfectly balanced edge that will never break or chip.
- Mithral: This weapon made of light silvery metal seems flimsy, but is strong and feels much lighter than other weapons of similar make.
- Cursed: Upon picking up this weapon you are filled with a sense of dread and bloodthirst, and your will is seized upon.
Whatever your preference.
It's never explicitly stated anywhere as far as I know. Some people think it breaks with immersion, while others think that you'll go crazy if you can't call out the numbers or keep having to talk around them.
Most people I know and play with refer to gear with their mechanical terms (ie: "My +1 Orcbane Shortsword") when talking to fellow people in the know (like their party-members, item creators or merchants) and in flowery terms when talking to laypersons (to a peasant it would be "My magic sword thirsts for the blood of orcs").
So in that regard, I think many people treat it like technical jargon: you use short, descriptive terms with people who understand them and you explain it to people who don't.
If magic items are a bit more common in your setting, you could also treat it the way talk about their phones.
ie; "You only have a +2 Longsword from Golem Inc? I just bought the all new +3.5 Special Edition Longsword from Pear Corp. Get with the times, loser."
Considering that the "plus" of the enchantments is a quantifiable attribute when identifying items or creating magical items I would imagine it reasonable that some manner of describing this attribute would exist in the game world. For the sake of simplicity I would stick with the +1, +2, +3, but other ways of describing would exist. Maybe even it's own term like carat or proof exists to describe it's "plussiness."
TLDR If a wizard can empirically determine the plus enchantment of a weapon you should be able to communicate that in the game world.
Whichever you prefer (or, to better say, whichever your DM preferes), but Magic Item Compendium p. 5 quotes Thordek, the iconic dwarf fighter, naming his +3 armor by plus and bonus.
It's not unreasonable to suppose that, in a world where enhancements come in fixed chunks, merchants and crafters have deviced a system to name them.
My personal choice is talking about "enchanted thrice" or "with a grade three defensive boost", without involving the plus.