A Vigilance ship boosts by Conclave should have no trouble scrapping ships in the battle phase by the 2nd Round. When talking pure Energy, no Strike Force ship will rival Vigilance, and Conclave can give out temporary shield boosts for the Battle Phase or when you think you might be taking a good deal of energy damage during aftermath flipping.
Both the Claw and Wrath have crazy movement and can well handle themselvs in sectors and bolt if things get too hairy. Finding a Cloaking Drive for Wrath early can be HUGE to 1) mill through her deck at blinding speeds 2) protect her energy until her shields can take things head on. If you play her right and draw lots of cards during the [R] and [I] phases, she builds faster than just about anyone. Buy as much as you can with her since you can mill through it so fast.
In the battle phase, Hit and Run/Deadly Focus with Ramming Speed for Claw can snipe off most Opposition ships outright. Focus on his Weaponry and keep his shields in a healthy place (around 4-5 on average). Claw loves suicide missions, so send him in, do your thing, then bolt out of the sector if you think it would be too dangerous to stay there.
Claw and Wrath's movement allows you manipulate the sectors station cards you abandon easily, so you can kind of plan exactly what the Opp will flip in the Aftermath and tailor you game plan accordingly. If the sector you are trying to lock down gets too hairy, Use Goated Pursuit and move all those Opp ships into the abandoned sector! Clumped up Opp ships means less bad stuff flipping in the Aftermath, but it makes the endgame a little rough, so use the free time to keep building.
EDIT: In this case, putting Wrath, Vigilance and Conclave in one sector with 3 ships and sending Claw into the sector with 2 ships might be your best bet. The first sector wont flip any cards in the Aftermath that way, and If Claw can scrap one ship and engage the other off the bat, none flip there either (or just 1 in the worst case senario). Your first 2 rounds will really set the tone of the game. Do everything you can to minimize the bad stuff while you keep chipping away and building up.
Once you play a few games, you will start remembering which station cards flip the worst Opp sides. For me, If I see Quasar Guns on the board somewhere and its in danager of flipping, you best be sure I will try and buy that up regardless of whether I need it or not (it flips into Mega Teleporter) Use this knowledge to your advantage. (I can't in good faith recommend cheating, but if you need to peak at the Opp sides while learning the game, I personally wont hold it against you)