An Esrog with a hole without a missing piece:[1]

Size of the hole: If there is a hole in the Esrog without any piece of the Esrog missing, such as a hole that was created by sticking a large needle into the Esrog, then if the hole of the Esrog is less than the size of an Issur it is valid. If the hole is an Issur or larger then it is invalid.[2] However there are opinions which rule that even a hole that is larger than an Issur is valid so long as no piece of the Esrog is missing. Practically one may rely on this opinion if there is no other Esrog available and one may use it with a blessing.[3]

The law if the hole goes from one end to another:[4] If the hole penetrates from one area to another area, the Esrog is invalid even if the hole is a very small amount and does not go from end to end.[5] However there are opinions which rule that even a hole that goes from one end to the other is valid so long as no piece of the Esrog is missing. Practically one may rely on this opinion if there is no other Esrog available and one may use it with a  blessing.[6]

The law if the hole reaches the seed box:[7] Some opinions rule that so long as the hole does not go from one end to another it is valid even if it reaches the seed box.[8] Others rule that if the hole reaches the seed box the Esrog is invalid even if the seed box itself and the other side of the Esrog remain untouched by the hole.[9] Practically we rule like the latter stringent opinion and the Esrog is invalid however if no other Esrog is available one may rely on the first opinion and use it with a blessing.[10]

 

Summary:      

No piece missing from Esrog:

Valid even initially: If the hole does not reach the seed box or go from side to side and is smaller than an Issur it is even initially valid.

Valid with blessing if no other Esrog available: If reaches seed box or goes side to side or is size of Issur.

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[1] 648/3

Source of these invalidations: All of these invalidations of a hole, and crack is not due to Hiddur but rather because the Esrog is not considered Tam [complete] and the Torah states “Ulikachtem” and the Sages expounded this to mean a full and complete taking. [648/14]

[2] 648/3

[3] 648/9

[4] 648/4

[5] 648/4

[6] 648/9

[7] 648/5-6

[8] 648/5; The reason for this opinion is because the hole is not considered Mefulash unless it goes from one end to another.

[9] The reason for this opinion is because the hole is considered Mefulash if it reaches the seed box even if it does not go from one end to another, as the seed box is considered like the other side of the Esrog. [648/6]

[10] 648/6