Are there buses fro Vilnius, Lithuania to Olsztyn,Poland? I will be going end of April.
There almost certainly is no direct bus link, but if you really wanted to sling together a bunch of bus connections, you could probably do it.
It may be easier to go by rail. You can take a train from Vilnius to the Polish-Lithuanian border, then exchange trains. There probably isn't a direct link from here, but the main rail route to Warsaw stops in Suwalki, which links to several other cities. You can probably get to Olsztyn from here, although I won't pretend to know how! You should probably allow for a full day of travel for this endevour.
By the way, do you speak Polish or Russian? It may come in handy here, because in this region, English fluency is rare.
You can take the Eurolines bus from Vilnius to Suwalki (3:15 hrs, www.eurolines.pl) and from there take a 5 hours direct train connection to Allenstein (Olsztyn; check www.bahn.de)