The Villafranca catalog of Galactic OB groups. II. From Gaia DR2 to EDR3 and ten new systems with O stars

CONTEXT. This is the second paper of a series on Galactic OB groups that uses astrometric and photometric data from Gaia and spectral classifications from GOSSS and LiLiMaRlin. The previous paper was based on Gaia DR2, this is based on Gaia EDR3. AIMS. The two aims of this paper are to revise the results for the sample from paper I using Gaia EDR3 data and to expand the sample of analyzed stellar groups to 26, from Villafranca O-001 to Villafranca O-026. METHODS. We use GOSSS to select Galactic stellar groups with O stars and an updated version of the method in paper 0 of this series, combining Gaia EDR3 G+GBP+GRP photometry, positions, proper motions, and parallaxes to assign memberships and measure distances. We present 99 spectra from GOSSS and 32 from LiLiMaRlin for stars in the analyzed groups or in their foreground. RESULTS. We derive distances to the 26 stellar groups with unprecedented precision and accuracy, with total uncertainties <1% within 1 kpc and of ~3% around 3 kpc, values that are almost 4x better than for Gaia DR2. We provide homogeneous spectral types for 110 stars and correct a number of errors in the literature, especially for objects in the Orion nebula cluster. For each of the groups we discuss its membership and present possible runaway/walkaway stars. At least two groups, Villafranca O-O12 S and Villafranca O-014 NW, are orphan clusters in which the most massive stars have been ejected by dynamical interactions, leaving objects with a capped mass function. The existence of such clusters has important consequences for the study of the IMF, the distribution of SNe across the Galaxy, and the population and dynamics of isolated compact objects. We fit PMS isochrones to four clusters to derive ages of 2.0$\pm$0.5 Ma for the sigma Orionis cluster, 4$\pm$2 Ma for NGC 2264, 5.0$\pm$0.5 Ma for NGC 2362, and 8$\pm$2 Ma for the gamma Velorum cluster. [ABRIDGED]