Can monsters effect that are sent to the graveyard by magic and trap card be activated?

Yes, they can! While monsters destroyed by spell or trap effects do not activate their effects because they are not treated as sent to the graveyard (instead they are banished), those monsters that are specifically sent to the graveyard by the effect of such spells or traps can activate their effects.

Examples:

* Mystical Space Typhoon destroys a monster on the field, so that monster will not activate its effect.

* Compulsory Evacuation Device bounces a monster back to the hand, so it will not activate its effect.

* Pot of Desires banishes the top cards from your deck equal to the number of cards you draw to the graveyard, any monsters among them will not activate their effects.

* Dark Bribe lets the opponent pay cost to negate a spell on the field and send it to the graveyard. In this case, monsters would activate their effects.