Which animal/bird/insect best describes such situation?

 - X is looking for Y.
- Z is also looking for Y.

And
- W makes Y available to both X and Z.

I am looking for a name of animal/bird/insect who are facing such situation in their food chain. It would be great if someone provide names of W,X,Y and Z.

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[Note: I will answer expecting that your question isn't a homework, because as I have told I find it very interesting. But in case it is, I wouldn't show your teacher these rambling divagations I'm going to write here, teachers frequently expect that the answers are centered on their local area, so...good luck if you use this material...].
[Note 2: I think that in marine habitats this type of situation is more frequent given that there are many more intermediate predators than in terrestrial habitats].

Such as you have posed it, I don't remember any direct example of two different insectivore birds looking for the same kind of insect, and an aditional element (W, you don't specify wether W is a bird, or even an animal) making those insects avalaible to their predators.

But I can tell of some similar situations:

1)  W accidentally or as the collateral result of its activities makes some preys accessible to some predators. There are a bunch of situations of this kind occurring in many ecosystems everyday, to tell you about some:

•   W is a maize farmer who uses flood irrigation methods. Y are some   different types of flies (Diptera) that lay their eggs in the flooded fields of W. As a result massive quantities of adult flying insects are avalaible for many insectivore birds, migratory ornot, such as sparrows, swifts, swallows, bee-eaters, etc, etc. They are yor X and Z (and the rest of the alphabet, and more :)).

• W is a bird that accidentally disperses invertebrates out of their habitats, burrows or even hosts. Thus these inertebrates are made available for some predators that live/chase well far from those habitats and biotopes, and that in other case wouldn't have very few chances of preying on them.

To give them name, W could be piscivorous birds, Y propagulates, and X pelicans.

There is a very interesting paper about the importance of birds as invertebrates dispersers in arid Australia: Page on ebd.csic.es.

2) W voluntarily tells X and Z the location of Y in order to get access to Y or some products of Y.

Honeyguides are named for a remarkable habit seen in one or two species: they guide humans to bee colonies.  Once the hive is open and the honey is taken, the bird feeds on the  remaining wax and larvae. This behavior is well studied in the greater honeyguide; some authorities (following Friedmann, 1955) state that it also occurs in the scaly-throated honeyguide, while others disagree (Short and Horne, 2002). Despite popular belief, there is no evidence that honeyguides guide the honey badger.

I give it up to you to name X, Y, Z, W in those cases.