Question: Does the Greek text of 2 Tim. 1:16-18 imply that Onesiphorus had already been dead by the time of writing these words?:

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> The Lord give mercy unto the house of Onesiphorus; for he oft
>  refreshed me, and was not ashamed of my chain: But, when he was in
>  Rome, he sought me out very diligently, and found me. The Lord grant
>  unto him that he may find mercy of the Lord in that day: and in how
>  many things he ministered unto me at Ephesus, thou knowest very well.
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Answer: 
I think that we need to understand firstly that Paul is contrasting Onesiphorus and his household with those people he mentions in v14. He is commending them for their care of him. 

The fact that it is just Onesiphorus' household that Paul speaks of in v15 and not Onesiphorus himself suggests that he wasn't there at the time. That might mean that he was dead, or it could simply mean he was elsewhere, after all Paul refers to the household of Stephanas in 1 Cor 16:15 when he is very much alive (just not at home 1 Cor 16:17)

It is easy to read a lot into the term "The Lord grant mercy to" in v15 and conclude that Paul was praying for comfort for the household. But that is not what he says. Notice in v18 he also prays for mercy for Onesiphorus as well and it doesn't seem to me that praying for mercy for one already dead would fit with Paul's theology. Paul is always praying/ asking for mercy or grace for people. Many of his letters open with such a prayer: Rom 1:7, 1 Cor 1:3, 2 Cor 1:2, Gal 1:3, Eph 1:2, Phil 1:2, Col 1:2, 1 Thess 1:1, 2 Thess 1:2, 1 Tim 1:2, 2 Tim 1:2, Tit 1:4, Phm 1:3 

In the end the evidence is not conclusive either way, so it seems clear that Paul presumed Timothy would know the situation, and that beyond our own curiosity the question does not have a great significance. By that I mean that we should not build a doctrine upon this as a key text, or even use it as a proof text for 'prayer for the dead' etc. The ambiguity precludes it's worth to that end.
I think the question misses the point. It seems logical that Paul prays for mercy for Onesiphorus not because he was already dead, but because he too had turned away and abandoned Paul like the others. Rather Paul, not wanting O. to fall under God's judgment for this act, prays that God will have mercy on him and remember his many kindnesses on Paul's behalf.