To clarify future inquiries, this does stack with a +X modifier of a weapon and/or ammunition.

Can you reference a source? 

https://www.sageadvice.eu/2014/12/05/arrow-1-bow-2-magic-bonus-stack/

Quote from abeltda >>

https://www.sageadvice.eu/2014/12/05/arrow-1-bow-2-magic-bonus-stack/

 This seems completely unrelated. The oil is for changing the bonus on an item. The bow and arrows are separate items with individual bonuses that go together. 

How is it unrelated ? Does the wording say it "becomes"? No it does not, bonuses stack unless the source specifically says otherwise.  It says it HAS a +3 bonus.

Jeremy Crawford clarified in his latest Dragon+: Basic Rules Updates 11/27/18 52:40.  New errata indicates that power potency does not overlap. Oil of Sharpness will not stack with another +X weapon.  

How many times can you use oil of sharpness?  Is it just a one use item?

Its like any other potion, it has a doses which are used once per melee weapon or once for every five arrows/bolts/darts 

The section of the book that JC and the errata refer to concerns a spell cast multiple times, not the interplay between a magic item and a potion applied to that magic item. 

What is the timestamp for that?

does the +3 add to an existent modifier on a magic item? or does it just overwrite any existent bonuses?

I'm pretty sure it would stack with a +X magical weapon. Effects do what they say they do. If the intention was for the oil to not stack with a +3 weapon the wording would reflect that. Either saying something like, "...has a +3 bonus to attack and damage rolls. If the weapon or ammunition already had a bonus to those rolls, choose which bonus applies", or "the weapon or ammunition becomes a +3 magical weapon or ammunition of its type".

My wording could be better but the idea is there, effects always stack unless they come from the same named effect. The dueling fighting style provides a +2 bonus to damage rolls which stacks with a +X weapon, because the bonus to damage is coming from two separate named effects. Similarly, the bonus from oil of sharpness comes from the oil and the bonus from a +X magical weapon comes from the weapon. If in the description of the magical weapon it said something like, "this greataxe has been coated in oil of sharpness, which makes it a magical greataxe and grants a +3 bonus to attack and damage rolls made with it", then it wouldn't stack with another coating of the oil, otherwise it's fair game. On the same vein, you would get no benefit from coating the same weapon in multiple coats of oil of sharpness at the same time.

The oil is also a very rare, consumable magic item, and +3 weapons are also very rare. Yes, consumables do tend to be less expensive than their non-consumable counterparts, but considering the equal rarity: if given the choice between a temporary +3 bonus to a weapon for 1 hour, or a permanent +3 weapon, you're very likely taking the permanent weapon. With that in mind, I think it's safe to allow the oil of sharpness its own moments of brilliance and push an already strong weapon to greater limits. Would it break the bounded accuracy of the encounter? Probably, but hey, it's just for an hour.

Dhampirs, remember to brush your teeth regularly... With oil of sharpness!

should I use this potion in a trade?

Can you quench a weapon in the Oil of Sharpness and if so what affect would it have, like would it give a permanent buff at a lower level like +1 or +2 or would it do nothing?

It is stated in the wording as you stated, it reads, "...has a +3 bonus to attack and damage rolls."  It doesn't say gains a stacking +3, or in addition to any current bonus' gains an increase of +3, it states only that it NOW has +3 to attack and damage rolls.  The "BONUS" word used is identical to all other 'bonus' wording to items, and is not specific to this potion granting a BONUS in addition to already had bonus'.   Thus a weapon with +1 bonus after applying the oil would then have a +3 Bonus as described by the item text, and would not grant further bonus.  Likewise if an item somehow had a +5 and then had this used it would reduce the bonus to ONLY a +3 as it changes the item to that state as described for the duration.

I wonder if this could be used as material components for a spell such as Hallow?