  We explore 6d (1,0) superconformal field theories with SU(3) and SU(2) gauge
symmetries which cascade after Higgsing to the E-string theory on a single M5
near an $E_8$ wall. Specifically, we study the 2d $\mathcal{N}=(0,4)$ gauge
theories which describe self-dual strings of these 6d theories. The self-dual
strings can be also viewed as instanton string solitons of 6d Yang-Mills
theories. We find the 2d anomaly-free gauge theories for self-dual strings,
amending the naive ADHM gauge theories which are anomalous, and calculate their
elliptic genera. While these 2d theories respect the flavor symmetry of each 6d
SCFT only partially, their elliptic genera manifest the symmetry fully as these
functions as BPS index are invariant in strongly coupled IR limit. Our
consistent 2d (0,4) gauge theories also provide new insights on the non-linear
sigma models for the instanton strings, providing novel UV completions of the
small instanton singularities. Finally, we construct new 2d quiver gauge
theories for the self-dual strings in 6d E-string theory for multiple M5-branes
probing the $E_8$ wall, and find their fully refined elliptic genera.
