TL;DR Helm shards work as follows
Rank 0: First seasonal legendary affix power
Rank 1: All Five affixes you would recieve from the 5 gems - Life% CDR RCR Gold% Xp%
Rank 2: One random affix (i.e. ~1000 main stat or up to 20% reduced melee/ranged attack damage)
Rank 3: Second seasonal legendary affix power
Rank 1 weapon shards follow the same gem mechanic like helms so +300 damage, +150% critical damage, +50% damage against elites, +30,000 LPH, +40,000 Thorns
Rank 2 weapon single affix can be up to +50% Damage, +75% specific element damage, +20% IAS, or +10% CHC
1/3 Helm shards and 2/4 Weapons shards are made for group meta, although one of those 2 weapon shards is usable solo
Soul shards you don't want can be used as level 50/75/100/125 augments based on their rank