Is there a way to cast integers to bytes, knowing these ints are in range of bytes. Using SSE?

The easiest way is probably to use pshufb to permute the bytes, followed by movd to store the datum:

        ; convert dwords in xmm0 into bytes and store into dest
        pshufb  xmm0, xmmword ptr mask
        movd    dword ptr dest, xmm0

        ...
        align   16
mask    db      0, 4, 8, 12, 12 dup (-1)

This stores 4 bytes instead of 3, so make sure your code can handle that. Storing only 3 bytes is also possible, but requires more work:

        ; convert dwords in xmm0 into bytes and store into dest
        pshufb  xmm0, xmmword ptr mask
        movd    eax, xmm0
        mov     word ptr dest, ax
        bswap   eax
        mov     byte ptr dest+2, ah

        ...
        align   16
mask    db      0, 4, 8, 12, 12 dup (-1)

If this happens more than once, you can load the mask ahead of time to avoid the penalty of repeatedly loading it.