"Cipher Soldier" and "Storm Cipher" are "Cipher" monsters by name, but otherwise are unrelated to the "Cipher" archetype's playstyle.
In cryptography, a "cipher" (or cypher) is an algorithm for performing encryption or decryption—a series of well-defined steps that can be followed as a procedure. However, the name of the archetype is written with the base 「光波」, meaning "lightwave".
Due to the additional requirement of the kanji in the anime compared to the OCG/TCG, "Cipher Soldier" is a member of in the latter, but not in the former.
Due to its use of Level 8 monsters to Xyz Summon Rank 8 Xyz Monsters, the "Cipher" archetype has synergy with the "Galaxy" archetype, which in turn has synergy with the "Photon" archetype. Because of the reliance on "Cipher Wing", it may therefore be wise to combine the "Cipher" archetype with the "Galaxy" and "Photon" archetypes, or at least with "Galaxy", to allow for more variety in combos.
The effect of "Galaxy-Eyes Cipher Dragon" allows the player to take control of one face-up monster the opponent controls and treat its name and original ATK as that of "Cipher Dragon". Not only does this decrease the number of monsters that your opponent controls while increasing the number of monsters you control, but you can also use the monster you took control of as a Tribute or as a Fusion, Synchro or Xyz Material, preventing your opponent from regaining control over it at the end of the turn; particularly if the monster you took control of is an Xyz Monster, it can be used as Xyz Material to Summon "Galaxy-Eyes Cipher Blade Dragon", "Galaxy-Eyes Full Armor Photon Dragon" or "Number 95: Galaxy-Eyes Dark Matter Dragon" through their effects. "Neo Galaxy-Eyes Cipher Dragon" can take control of up to three face-up monsters your opponent controls and make their ATK 4500.
Once "Galaxy-Eyes Cipher Dragon" has been successfully summoned, the focus of the archetype switches to protecting and supporting it. "Cipher Mirror Knight" can be used to revive it if it has been destroyed, and "Cipher Spectrum" can do the same if it had an Xyz Material attached to it, in addition to Summoning another one from your Extra Deck. If you control a "Galaxy-Eyes" or "Cipher" Xyz Monster and your opponent controls a monster with higher attack, "Double Cipher" can be used to Summon another one with the same name. You can then use them to Summon "Galaxy-Eyes Cipher Blade Dragon", "Galaxy Eyes Full Armor Photon Dragon" or "Number 95: Galaxy-Eyes Dark Matter Dragon"; even if your opponent controls a monster with higher ATK, the former two can destroy it using their effects. In order to increase the Xyz Materials of your monsters, you can use "Cipher Bit" to prevent a "Cipher" or "Galaxy-Eyes" Xyz Monster from being destroyed by a card effect once and give it an extra Xyz Material, while "Cipher Etranger" can attach itself to a "Cipher" Xyz Monster as an Xyz Material.