Does MTL files refer to "Specifies the material library file for the material definitions
set with the usemtl statement.

Yes

You can specify multiple filenames
with mtllib. " from OBJ format?

I never tried it but I programmed it that way. You can also cite more than one mtllib line.

Is IGES easier to convert (by a python script I write) to OBJ so it can be used in SweetHome3D?
In other words, which of STEP or IGES is more like a .OBJ file used for a stretchable object in SweetHome3D?

I have no knowledge of STEP or IGES format. Please provide some links to documents that describe these formats for a CAD novice like me.

So far in Blender, my .obj exports always are given more triangles
so they become meshes rather than boundary-reps. Can you stretch a .obj model with many triangles in it in SweetHome3D?

I'm not sure if it's what you're talking about, but programmers generally implements exportation to OBJ format with triangles, even if nothing prevents from describing polygons in OBJ format (and Sweet Home 3D supports polygons joining more than 3 vertices).
In all cases, that doesn't prevent an OBJ shape to be stretched in Sweet Home 3D or any other software.