According to Symbols of NASA:
From the wing of the space shuttle to the top of the NASA homepage,
the agency's official insignia is probably its best-known symbol.
The round red, white and blue insignia, nicknamed the "meatball," was
designed by employee James Modarelli in 1959, NASA's second year. The
design incorporates references to different aspects of the mission of
the National Aeronautics and Space Administration. The round shape of
the insignia represents a planet. The stars represent space. The red
v-shaped vector represents aeronautics. The circular orbit around the
agency's name represents space travel.
And Wikipedia on NASA insignia adds that the red chevron is in the alternate shape of the constellation Andromeda.
As for constellations, they're highly stylized and not drawn to scale or apparent magnitude of stars and galaxies in constellations, but I'll go by what I recognize:
- Top one is Orion (Hunter), left brightest star is Rigel. Notice the Three Kings in the Orion's Belt and the Orion Nebula (M42) in the Orion's Sword.
- Bottom left one is Cygnus (Swan), the bottom brightest star is Deneb. Notice that it closely follows the shape of a swan in flight, albeit the apparent magnitude and position of other stars again seems rather random.
- Bottom right one is a tricky one but might be the part of Andromeda with the Andromeda Galaxy, or the part of Lyra with Vega, or more likely - simply some randomly painted stars.
Otherwise, there is no exactly such constellations or a groups of stars in the night's sky that would follow the triangle that the three groups on the logo represent. They all appear to be constellations that would appear on the Northern hemisphere night skies at least during some parts of the year (Orion for example isn't always visible or is too low on horizon at times), but they certainly don't represent the Summer Triangle between Deneb in Cygnus, Vega in Lyra and Altair in Aquila. I'm fairly certain about the Orion and Cygnus, alas, I fail to clearly recognize the group of stars on the bottom right of the logo.