National Action, labelled "racist, anti-Semitic and homophobic" by the former home secretary Amber Rudd, was banned in December 2016 after a series of rallies and incidents, including praise of the murder of MP Jo Cox.
Cutter, 23, who entered the Miss Hitler beauty contest as Miss Buchenwald - a reference to the World War II death camp - had denied ever being a member, despite attending the group's rallies.
Jurors were shown messages in which the waitress joked about gassing synagogues, using a Jew's head as a football, and exclaiming "rot in hell" after hearing of Cox's murder.
Jones, a former member of the British National Party's youth wing, was described during the trial as a "leader and strategist" who played a "prominent and active role".
The 25-year-old, originally the group's London regional organiser, acknowledged posing for a photograph while delivering a Nazi-style salute and holding an NA flag in Buchenwald's execution room during a 2016 trip to Germany.
Prosecutors described Cutter and Jones, both of Sowerby Bridge, near Halifax, West Yorkshire, as well as Jack and Scothern, as "active" group members, even after the ban.
Jack, 24, of Birmingham, had attended almost every meeting of NA's Midlands sub-group.
He also had a previous conviction for plastering Birmingham's Aston University campus with NA stickers, some of which read "Britain is ours, the rest must go".
Scothern, 19, of Nottingham, was "considered future leadership material" and had distributed almost 1500 stickers calling for a "final solution" - in reference to the Nazis' genocide against Jews.
Cutter was jailed for three years, while Jones received a five-and-a-half-year prison term.
Jack was sentenced to four-and-a-half years in prison, and Scothern was handed a sentence of detention for 18 months.
Speaking ahead of sentencing, the director of public prosecutions, Max Hill, QC, described NA members as "diehards" who "hark back to the days of not just anti-Semitism, but the Holocaust, the Third Reich in Germany".
