I call these guys the shizz. The Winnu have almost the same technology advancements as the Universities of Jol-Nar. You may always add the influence value of your home system to add to your vote. Your planets that have at least one ground force are immune to the Local Unrest Action Card. To top this off you do not need to spend a command counter to execute the secondary of the technology card. You also start with 3 technologies. As with all races that start with 1 carrier I suggest getting out right away and wait for the production card to be played before putting another carrier into play. That way you can still move and take another planet that first turn.
Spread yourself thin leaving only a single troop per planet since they are now safe from the local unrest card. Try to get the technology card the first turn if possible then let others get it and use the secondary ability. Save money because tech will still cost you but it will not cost you a command counter. When you do tap planets try to tap your home world first since the influence can still be used even while tapped.
Your starting technologies do not put you directly on a path to War Suns but they do help. If you are lucky enough to get a secret objective that involves technology you should have no problem taking over the world. As with any race try to keep the funds flowing and always have excess command counters allowing you free movement and secondary actions.