Burning
The Burning status can be applied by dealing Fire Damage to a character. When you apply burning status effect on an enemy, they take fire damage over time based on your Max Magicka and Spell damage. Burning effect lasts 4 seconds and ticks every 2 seconds.

Chilled
The Chilled status can be applied by dealing Frost Damage to a character. Chilled enemy suffers from Minor Maim debuff for 4 seconds, reducing their damage by 5%. If you also have an ice staff equipped, this will apply Minor Brittle.

Concussed
The Concussed status can be applied by dealing Shock Damage to a character. Concussed enemy suffers from Minor Vulnerability debuff for 4 seconds, increasing their damage taken by 5%.

Poisoned
The Poisoned status can be applied by dealing Poison Damage to a character. When you apply poisoned status effect on an enemy, they take poison damage over time based on your Max Stamina and Weapon damage. Poisoned effect lasts 6 seconds and ticks every 2 seconds.

Diseased
The Diseased status can be applied by dealing Disease Damage to a character. A diseased enemy suffers from Minor Defile debuff for 4 seconds, decreasing their healing received by 8%.

Hemorrhaging
The Hemorrhaging status can be applied by dealing Bleed Damage to a character. A hemorrhaging enemy suffers from Minor Mangle debuff for 4 seconds, reducing their maximum health by 10%.

Sundered
The Sundered status can be applied by dealing Physical Damage to a character. A sundered enemy suffers from Minor Breach debuff for 4 seconds, decreasing their physical and spell resistance by 2974.

Overcharged
The Overcharged status can be applied by dealing Magic Damage to a character. An overcharged enemy suffers from Minor Magickasteal debuff for 4 seconds, which restores 168 magicka per second to players dealing damage to them.

From Uesp Wiki

Status Effects stack additively in MOST cases.

So like using the initial hit of Engulfing Flames on an Inferno Staff magDK wearing Heartland Conqueror as an example, you would have an AoE Direct Damage skill with a base chance of 5% * (1 + 1 + 4.4 = 6.4) = 32%. The subsequent Engulfing Flames DoT would have a base chance of 3% * 6.4 = 19.2% per tick. I don't actually know how the game handles decimal numbers but I would suspect that it rounds down to the nearest whole number.

However, some abilities have an entirely separate multiplicative term at the end of their calculation, such as Pulsar. For a Pulsar tick, you would have a base chance of 5% * 6.4 * 4 = 128% per tick chance. [EDIT: used correct multiplier of 4, up from 3. Status Effect stacks additively within this final term (e.g. 1 + 3 = 4)]. The same principle operates for the Warden's Winter's Revenge skill though that is an AoE DoT so, of course, the base chance begins lower.

I hope that that clarifies things.

To answer your question though, nothing will compete with Precise and stacking Critical Damage in PvE until something is done about either the extreme levels of Critical Damage that are able to be stacked or alternative means of dealing damage (such as Max Stats and Weapon/Spell Damage) are buffed into competitiveness.

But if you're talking PvP then the possibilities open up considerably.

[EDIT: to include the correct multiplier evaluation for Pulsar and related abilities.]