Comparison of carbocation stability in bicyclo compounds
I think the third option as greatest number of resonance structures can be alluded to it.
The following may suffice:

In the first one, the carbocation is isolated except for the presence of a single double bond in conjugation beside it. The oxygen and the double bond beside it play no role in stablizing it.
In the second one the lone pair on oxygen, the double bond and the carbocation are in conjugation. Hence, it is somewhat stable.
In three, similar conjugation like two is present, but is it extended over another double bond i.e. the lone pair of oxygen, two double bonds and the carbocation are all in conjugation and an extended resonance comes into play. Thus, it is more stable than two, since more number of resonance structures may be drawn for it than 2.
The fourth one is the least stable among them, as no conjugation or resonace structures may be constructed. Moreover the I- effect of the neighbouring oxygen tends to destablise the carbocation.

Hence, the order of stablity:
3&gt;2&gt;1&gt;4
An arrow-pushing representation of resonance in the third option can be made as follows:

Hope it helps.