I'll outlay the most common ways to MISUSE Silence:
1- Everyone whose abilities you Silence are on Cooldown (easiest against people with lots of Ranged abilities, Occulus, TB)
2- Using Silence 1v1. Most demigods will say "You Silence, I kill you" in a 1v1 fight
If you silence everyone while on cooldown then you just completely wasted mana (and Silence is not cheap).
Silence is rarely useful 1v1. The ONLY time I Silence 1v1 is to cover up a lock or a port (Silence II guarentees a port out from everyone. Silence I guarantees a port out from every skill except Penitence, Deep Freeze, Grasp, Swap and Silence (cast time is instant. So that leaves Mass Charm, Frost Nova, Pounce, Boulder Roll)) or against a UB.
Why UB? Most UBs will learn that you will Heal III of their spits so they'll save it, alternatively, they'll try to grasp you as soon as they spit (or guess you will heal). If they are saving their grasp and Spit, Silence buys you time to delay those abilities another three seconds and lets you heal safely. Then it breaks the rhythm of spells and helps you out a bit. However, you have to be very careful about this. I have Silenced "once too much" and run out of mana for a crucial heal.
You should use Silence as the first ability whenever you port in or you get ported on (especially when multiple people come). 2 people porting on you and a buddy on the HP flag will typically result in you winning the skirmish when you get to unload your abilities and they don't.
Once you level up Magnificent Presence, you can Silence at the beginning and end of the battle, and sometimes even three times in hectic ones.
The other best time to use Silence is to prevent sigils. I will Silence-Pounce and then my buddy will do whatever burst damage he has and finish them off. Counter Healing means that monks won't throw it off.
You can also use it to link Stuns: Your UB stuns a target, then your Erebus starts casting Charm while he is grasped so he remains stunned. While this is happening you walk forward to cover both the opposing Oak and the targeted demigod and drop Silence. Now he is shield-less, sigilless. This works especially well against Erebus who becomes dreadfully overexposed once he has no Bite, no Mist, no Mass Charm and no Batswarm.
If you get max out Magnificent Presence and get the opponent's Celerity flag a wonderful thing happens: you can perpetually stun/Silence. It drops all 15 cooldown stuns (Silence, Frost Nova, Grasp, Boulder Roll) to 9 seconds. Boulder Roll (2.5) -> Grasp (2) -> Silence III (5) and by the time Silence wears off, they are Boulder Rolled again. You can't quite perpetually do it if you don't have the Celerity flag, but they only have roughly a 1.5 second window.
Once you have max MP and Pounce, you can guarantee a kill against all not-faster-than-you Demigods: The second they hit ~2.2k, Pounce, Silence, autoattack and Pounce again when it comes off of cooldown (4.5 seconds to Silecence's 5 second duration). However, it is difficult to do this against most characters because you have to invest in Inner Grace in order to properly chase most demigods.
Sedna versus Sedna Silence typically goes to whoever wins first, but you have to be careful how you time it. Sedna versus Sedna is very very fun (for me) partially because it is so rare. Builds that work very well against most tier 1 demigods aren't as effective against Sedna mirrors.