From the earliest days of fantasy role-playing, there have been various creatures that were completely immune to attacks by non-magical, non-silvered weapons. Such creatures are supposed to be a normal part of the milieu, but a kind DM will make sure they the PCs don't meet them until the party has at least one magic weapon.
While this helps with game balance, it also lacks verisimilitude. Why would these creatures stay away from characters who were least able to fight back? Being generally evil and predatory, they would likely look for easy targets.
Throwing a magic weapon or two at the party was one way around this, but that could lead to power inflation early on. On the opposite side of the coin, if only one character had the weapon in question, then the other characters really couldn't participate in the encounter. True, spellcasters with the right spells could help, but there was no guarantee that those spells would be in their arsenal.
"3E D&D" tried to get around this with damage reduction, though that usually meant that the first 15 points of damage were ignored. In effect, the creatures were immune to harm, as even the mightiest barbarian would be unlikely to hurt it. "3.5 D&D" dropped the distinction between magic weapons of various pluses and simplified it to "magic." Gone were creatures that were only hurt by magic weapons of "+2 or better." This really didn't solve the problem, but it helped simplify things a bit.
So how does one overcome the impossibility of an encounter with an immune creature when the party is ill-equipped for it? One way is to allow the characters to capture it, unharmed but overwhelmed by sheer strength. Tied up or placed in a cage, the creature would pose little threat and might bargain for its freedom. Threatening it with drowning might also work. There could be whole adventures based around hog-tying a gargoyle an bringing it back!
The Moldvay "Basic D&D" book suggested that one creature with weapon immunity could harm another, such as a werewolf harming a shadow, and vice versa. Another option was to let a creature with more than 4 hit dice (level) overcome the resistance. An owlbear was therefore able to harm the werewolf as well. Ogres, with their 4+1 hit dice, should probably be included in the "greater than 4" category - if only because the monster attack matrix has "4+ to 5 hit dice" as a separate attack class from 4 hit dice only.
Perhaps Fighters, and only Fighters, could be allowed to harm these creatures at level 5. At name level (9th), they could hit creatures normally only hit by +2 weapons or better. This could distinguish the class in a way that gives them some excellent combat mojo without really harming the game.
A more universal solution might be to allow normal weapons to do only half damage, or to reduce the damage die by one or more. Thus, a sword (1-8) might do 1-6 or even 1-4 damage. Silvered or magical weapons (as the creature's nature dictates) would simply do full damage, with any pluses added in. You can still distinguish between creatures that are only hit by +1 weapons vs. +2 weapons with this method if you like; +1 weapons will still do an extra point of damage on top of the reduced damage rate.
Damage reduction can also be brought back, but in a lesser form. For example, it could be DR5 for +1 monsters and DR10 for +2 monsters. This gives most parties a chance to at least do some damage. DR4 and DR8 might also work, these are the maximum (unmodified) values for a dagger and a sword, respectively. It seems fitting to say that "+1 monsters" cannot be harmed by daggers (barring strength bonuses), and "+2 monsters" cannot even be harmed by arrows or swords!
Finally, one can simply increase the armor class of such monsters, perhaps by 3 per "plus" of resistance. Thus, an AC5 gargoyle could have its AC improved three steps to 2 if the party lacks a +1 weapon, while a monster that requires +2 weapons would improve its AC by six steps. Damage would be full if the attack does hit. For game systems that don't use armor class or its equivalent, the attacking characters could suffer a commensurate penalty to attack rolls.
Any of these methods allow the otherwise immune monsters to be included in an encounter, regardless of the party's capabilities. Be sure to give the PCs extra experience for winning an encounter with such a disadvantage - even if it means using a weaker creature, then granting the full XP value for the higher level characters.