Solemn

[Pandariel]

can i strike cards like brilliant fusion, invocation and monster reborn? or only warning them?

[MadRest]

Solemn Strike cannot be used to negate the activation of a Spell/Trap Card. It also cannot be used when a monster would be Summoned during the resolution of an activated card/effect, so it can't do anything against those cards.

Solemn Warning can negate their activations, and that is the only thing thing it can do to them.

[MadRest]

Madrest you mean it cannot be used when a monster "is summoned" during the resolution of an activated effect. There is no attempted summon to a card resolving it's effect, because it is always successful if the source of summon is not negated.

You cannot solemn strike, because the monster is not classified as "when be special summoned" as per it's own method of summoning that doesn't start a chain (Such as Chaos Sorcerer), but rather from one that will successfully summon the monster if allowed to resolve with effect (such as brilliant fusion). Once resolved, the monster is successfully summoned, so the "When a monster would be summoned" condition is not met, because it's already on the field by this time.

Solemn warning is allowed to the source of summon or summon attempt of a monster. For this you have to negate the source of summon, in short Brilliant Fusion, Invocation, Monster Reborn. You cannot solemn warning the monster's summon to the field (again) because it's successfully summoned at resolution of Brilliant Fusion, Invocation, Monster Reborn. Since it's successful, it's already on the field, and doesn't meet the "when a monster would be summoned condition".

To meet this condition, it has to be when the monster's attempted summon is conducted, such as an off chain special summon attempt (Chaos Sorcerer).

You're misunderstanding something. The reason those kinds of Summons are always successful is because the "would be Summoned" period occurs in the middle of the effect's resolution, so nothing can be activated at that time (but that period of time still passes). This is hypothetical, but it is theorized that if a Summon-negating Continuous Effect existed, then it would be able to negate even Summons that occur during an effect's resolution.