You can only use the volley with ranged weapons that use ammunition
The volley has two conditions for its use
- it must be a ranged attack
- it must use ammuntion
You can use your action to make a ranged attack against any number of creatures within 10 feet of a point you can see within your weapon’s range. You must have ammunition for each target, as normal, and you make a separate attack roll for each target.
A pure melee weapon, such as a glaive, can not be used for the volley, as it violates both conditions.
While some melee weapons, such as a dagger, light hammer, or handaxe have the thrown property, which allows you to use them for ranged attacks, they do not have the ammuntion property, so even those weapons cannot be used for a volley. Page 146, PHB:
Ammunition. You can use a weapon that has the ammunition property to make a ranged attack only if you have ammunition to fire from the weapon. Each time you attack with the weapon, you expend one piece of ammunition. Drawing the ammunition from a quiver, case, or other container is part of the attack.
While this is the technical rules-as-written answer for thrown weapons, check with your DM. They may be up for allowing you to throw multiple daggers or such, in case you have them in a belt to throw. This should not be unbalancing, as a bow tends to deal as much or more damage than these weapons, and either one will suffer disadavantage if used in close combat, so it is more of a flavor question to allow this or not.