Aum is to be used always before all the Gods.
Shree is The Respect title for addressing us to the Gods.
Kreem is not necessarily for Asuras as far as I am concerned.
Aum is the Embodiement sound of the Unmanifest. Omkara is both Shiva both Vishnu and related to all the Devas.
Shree is usually put as Higher the consideration of That Swaroopa or Deva is.
Shree Ganesha and
Are the Examples also
Of course Shree Shiva may exist but usually I have heard:
Shiva is Sada Shiva
Such as Shakti is Para Shakti
In many mantras and stotrams.
While I have heard:
Shree Ganeshaya Namaha
Shree Guru Charana Sarooja Rajanija
In the first Doha of Hanuman Chalisa, referring to Hanuman as Shree.
But until now Shree Shiva in the mantras, shlokas or shatakams in Sanskrit it is more rare.
The majority of these dedications to Shiva involves synonims or other names of Him by using Sada Shivaya as to refer to Him respectfully.
But by using logic, one can state Shree Shiva could be used as to address to Shiva.
While we can consider Shree Vishnu as like Shreeman Narayana
Shree Pratyagiri also, which is a Form of Maa Lakshmi when Vishnu became Narashima.
Kreem, Klim, Gloum etc are all Syllables to call for a Quality Task associated with Devas or Gods.
Examples in Chamundaye Vicche mantra
Because She destroyed Chamunda Asuras we chant
Om Aim Hreem Klim Chamundaye Vicche, which Syllables after AUM, do refer to what She do and perform in that situation, repeated into similar situations.
Other and most beautiful example is Shiva Maha Kalabhairava Stotram
" Yam Yam Yam Yaksha Roopa "in which any each one of the syllables call for a task and a quality and a ability of Sada Shiva. See the link below
Also Na Ma Shi Va Ya itself do refer to Elements.
The beejas = seeds sounds do associates with all the chakras too.
Macro and Micro Cosmo Balanced through Devotion Bhakti to the Gods.
This answer from another user: https://hinduism.stackexchange.com/a/19446/22667