Can I ask God to avenge my enemies?
David did it. His psalms many contains contents of asking for revenge.
So, it is justified to ask God avenge my foes.
I agree with you that, in the OT, Israel can be seen to be very revengeful. I recall the Psalms that was sung by Boney M, "Rivers of Babylon", that talks about grabbing the infants of the enemies of Israel and smashing them against the rock.
That was why Jesus caused such a stir when he first taught the Sermon of the Mount, urging Israel not to respond like for like. If I am a Jew then, I would clearly find Jesus very difficult to understand, after being brought up in the OT.
But for us in the Body of Christ, Paul, our apostle, has a specific instructions regarding this in Romans 12
14 Bless those who persecute you; bless and do not curse. 15 Rejoice with those who rejoice; mourn with those who mourn. 16 Live in harmony with one another. Do not be proud, but be willing to associate with people of low position.c]">[
c] Do not be conceited.
17 Do not repay anyone evil for evil. Be careful to do what is right in the eyes of everyone. 18 If it is possible, as far as it depends on you, live at peace with everyone. 19 Do not take revenge, my dear friends, but leave room for God’s wrath, for it is written: “It is mine to avenge; I will repay,”d]">[
d] says the Lord. 20 On the contrary:
“If your enemy is hungry, feed him;
if he is thirsty, give him something to drink.
In doing this, you will heap burning coals on his head.”e]">[
e]
21 Do not be overcome by evil, but overcome evil with good.
So the clear answer is, No, you should not.