Can I get married immediately after her oath taking/citizenship approval?

Generally, when a U.S. citizen (who became a citizen by birth or by naturalization) becomes married to a foreign national who entered the U.S. lawfully and with inspection, the couple may succeed in a marriage-based Immediate Relative application to adjust status by which the foreign national will seek to become a Lawful Permanent Resident (to get a "Green Card"). This is true regardless of whether the marriage took place before or after the date of naturalization. Since one becomes a U.S. citizen instantly upon completion of naturalization, a marriage-based adjustment of status case may be filed the very moment after completion of naturalization. Although not completely clear from your description, it sounds like your most recent entry into the U.S. resulted in you being admitted into the U.S. following "secondary inspection" at the airport. You entered on a B1/B2 visa, which required "nonimmigrant intent," i.e. an intention to remain in the U.S. only temporarily. Becoming married to a U.S. citizen and filing a marriage-based adjustment of status application very soon after entering the U.S. can be viewed by the USCIS as demonstrating "immigrant intent," i.e. an intention to remain permanently. Entering with a B1B2 visa while intending to remain permanently can be viewed as "visa fraud," which can have very serious immigration-related consequences. If you entered the U.S. with nonimmigrant intent, then became engaged to be married with a newly formed intention to remain permanently, that may be satisfactory. Becoming married and applying for adjustment of status more than 3 months/90 days following entry should eliminate an inquiry about whether an applicant fraudulently used his/her B1/B2 visa. Of course, there also are many other details that have an impact upon immigration eligibility. It would be wise for you and your fiance to consult with an immigration attorney who, after learning all of the relevant information, could advise about eligibilities, options and strategies to attain your goals, and who then could offer legal representation in the often complex application process.