Somehow oil is getting into the air filter assembly on my '05 V-Star 1100 Custom.

back fire,bogs down and choke required means it is lean.
Check fuel filter, fuel tap
intake air leaks, loose clamps, cracked rubber
vacumn hose off
valve clearance
loose jets in carb \dirt in carbs
part of a carb coming loose , like the top cap

The back fire can be because of carbon fouled plugs, caused by the choke on.
air intake leaks can sometimes be found by spraying WD around intake rubbers,while running and listening for engine change.
The rest is mainly visual inspection and adjusmnet

bad seal.

http://www.carlsalter.com/motorcycle-manuals.asp

free pdf service manual there for you

buy oil and filter from your dealer, they will know what you need, yes drain it, change filter and re-fill. job done, dont pay to get it done it's so simple and you will save about $85