You can find the currently known miRNAs at miRBase: http://www.mirbase.org/.
You can download all of them in one file (http://www.mirbase.org/cgi-bin/mirna_summary.pl?org=hsa look at the bottom of the page).
With the sequence file you can create a BLAST database.
http://www.ncbi.nlm.nih.gov/books/NBK1763/ use makeBlastDB or formatDB for that.
Finally you can blastn your candidates against the database and you will find similar miRNAs.
In my opinion, what you should do as well is to predict the targets for the viral miRNA within the human genome. Viral miRNAs can regulate host gene expression so that is a very interesting question for you.
In that case you can just follow the steps on top and use mirTarBase (http://mirtarbase.mbc.nctu.edu.tw/) to see the targeted genes for the miRNAs you find using BLAST. In that case you need some luck since there is no guarantee that the miRNA's targets are actually in the database.
Following that use the sources and targets you found and check them in KEGG to see if any of the pathways make sense in respect to the disease caused by the virus.