Hilchot Shevuot

General

1. An oath to perform an action cannot override a preexisting oath, neither to strengthen it nor to negate it. At the same time, each additional Shevuah is queued and held dormant until one seeks to annul the first one. Then, the second one will take effect. Therefore, one must seek annulment for each oath taken. For this reason, the Ben Ish Chai suggests, the text of Hatarat Nedarim repeats the annulment numerous times, to cover any potential repeat oaths.
2. Meanwhile, every oath taken to testify that an event occurred is an additional independent violation of the Torah's command to not take a false oath.

Davar Mitzvah

1. An oath taken not to perform a Mitzvah is ineffective, because an oath cannot override a preexisting oath, in this case, the obligation to do Mitzvot, which we accepted at Har Sinai. If the oath was to not perform or to perform a Mitzvat Aseh MiDeRabbanan or a Mitzvat Aseh learned from extrapolations of Torah Shebaal Peh, it is, however, effective, as a Shevuah Min HaTorah is stronger. On the other hand, swearing to violate a Mitzvat Lo Taaseh, albeit MiDeRabbanan, is ineffective, as one is already under oath to listen to the Chachamim. The Ben Ish Chai recommends that one still seek to remove the oath.

Hatarat Shevuot

See Hatarat Nedarim for the bulk of the laws.