if you file for asylum then you will be an asylee seeker , to answer your question in one line. but, keep in mind, less and less Nepali asylum cases are getting approved lately. you have an opt , that tells us that you've been in the us for more than 1 year. in most states other than sanfran ca, that enough is ground to deny your case , and that is done most of the time unless you have a very very solid proof for why not. i guess ppl in san fran are generous. if you pass that hurdle, and get approved , rmember when you're an aslyee you're not a Nepali , your passport or any other protection from Nepal or other country revokes your asylum status. if your case is not genuine they can always reopen your file and revoke your asylum, or premanet residency, even citizenship but usually they have to go to federal court to remove the citizenship and that costs lots of money and time for them so unless it's very serious they let the naturalized citizens slide. remember, with the green card you got from asylum they have category numbers starting from a5, a7 for spouses and a8 for derivative children and often asylees feel that they are treated like thieves from the immigration officers when they incounter them. if you go to Nepal and come back with those kinda green card , io at the port of entry gives your special treatmenat and if found that you went to Nepal, they can revoke your green card. so far lots of Nepalis are going via india, but that is technically wrong and if found guilty can have severe consiquences. plus India may stop taking refugee travel doc in the future and you will be compelled to use your Nepali passport which will revoke your asylum or not go to Nepal at all.  you are giving up your country , Nepal totally , keep that in mind. I thik that is a big big price to pay for if you absolutely don't have  very very good reasons to do that. 
Also, keep in mind that Nepali congress and Nepali student org were considerd as tier iii terro..orginazations by uscis few months ago, and most Nepali asylum, greencards and i730s (petition for asylee family members) were in indifinate hold, i don't know if that still continues, but be careful to that too. i recommend going thorough eb2, because you have no restrictions after you receive your gc. asylum means restrictions restrictions and more restrictions, and treatmenat like you're a theif because most IO think you're just sucking their public story but they are compelled to give you a status because of the law. be careful.. 
I am not an asylee  , the above lines are based on my experience from helping some Nepali daju /didi asylees last  year. please think carefully.