A sample of 34 dwarf irregular galaxies in the Local Volume, most nearer than 5 Mpc, has been imaged in the near-infrared (NIR) in J and K_s at CFHT in Hawaii and OAN-SPM in Mexico. In CFHT images, stars brighter than M_Ks=-7.5 were resolved. In most cases, the resolved population represents less than 5% of the total NIR flux in K_s. Although exponential at large radii, surface brightness profiles for the unresolved component flatten in the centres. They can be fitted across the whole range of radii with a hyperbolic secant (sech) defined as a function of two parameters: the central surface brightness and the scale length of the exponential. Isophotal, total, and fitted sech magnitudes have been calculated for all galaxies for which the unresolved component was detected, along with semimajor axes. The scale length and the semimajor axes correlate linearly with absolute isophotal magnitude. The same is true for colors and the central brightness. More luminous dIs tend to be larger, redder and brighter in the centre. The Tully-Fisher relation shows considerable scatter, but residuals are tied to surface brightness. The galaxies appear to lie in a ``fundamental plane'' defined by the sech absolute magnitude, the sech central surface brightness, and the HI line-width. The rms of residuals in M_K is only 0.4 mag, which implies that the plane can be used to evaluate the distances of star-forming dwarfs. Color-magnitude diagrams are presented for 29 galaxies in which stars were resolved. Most show a finger centered around J-K_s=1 mag. In some cases, there is a red tail extending to J-K_s=2.5 mag. (Abstract slightly shortened).

Accepted for publication in AJ. Full version including figures available at http://aries.phys.yorku.ca/~ovidiuv/Paper2.ps.gz