Question That needs answering

Well considering that you don't have Entrenchment (by the way it would be cheaper just to buy Entrenchment and Diplomacy seperately as that would only cost you $20 as apposed to $40 for three games in one when you already have one of them) I recommend building two fleets, use one for holding a bottleneck against the AI with repair bays to help (the other fortifications don't really do anything until they get a starbase to work with) while the other rampages behind enemy lines, wrecking economy and making the AI chase you, eventually the AI will weaken (especially because they will still send fleets at the bottle neck while trying to chase you weakening themselves quickly) and you can begin clean up easily.

No offense, but if you're so seriously destroyed by a well-timed invasion you're making some mistakes somewhere.

If you're playing with unlocked teams, then you have to make some allies.  If you aren't, then you're basically fighting a 3v1 (or whatever the settings are), and that's a much more difficult scenarion than you probably signed on for.  You can change the settings to "locked teams" which will prevent anyone from making alliances, or you can fight an AI in a 1v1 scenario.

Aside from that, you need to scout.  If the first thing you see of an invading enemy is them bombing your planets, it's too late to save them.  You need to scout and know that these attacks are coming so you have time to prepare for them.  As Ryat mentions, that may involve creating two separate fleets to defend two separate fronts.

It seems you have to be very aggressive and keep expanding in this game.

I'm pretty new and after losing the first few games, I found I need to keep pushing in early game, grab as many planets as possible and keep attacking.

You probably wasted too much resource doing this -  8 fully fortified worlds.

Probably better off to shore up the front line/ choke point and build as many ships as you can.

I build 3-4 repair bays, and 4-5 def platforms, that seems to be able to repel early game attacks, adding hangar when I can. I can hold off 1 on 1 (cap ship) fight and sometime 2 on 1.

You need to keep attacking to cripple their economy/ship building ability (destroy military lab.)

Just keep attacking and then retreat to repair your cap ship.

I only played mostly small and medium maps so far and this seems to work pretty well. As soon as I get the 2nd or 3rd cap ship, I can open a 2 front war and bleed the AI to death.

I think this can happen if the teams are unlocked--eventually all of the AIs will ally against you.  In my single player days this happened to me a couple times and I was always thinking, WTF?  Why are they all picking on me?!?  (Maybe unlocked games work out differently in the Diplomacy expansion now; I only play online against other people so I wouldn't know.)  The solution is to play the game with Locked Teams so that none of the AIs can form alliances with one another.

nope

Can't you pretty much force some of the AIs to be your ally with the diplomatic ships?  Wasn't that part of the entire point of the expansion?

hmmmm to be honest, never tried it

I have, I ally them all and watch them fight while I set up my novaliths(if Tec) or Starbases in every world(includeign theres) as Advent with evangelisim upgrades. "You have outlived your usefulness to my cause! you, and all your race shall be exterminated for this!  BWAHAHAHAHAHAHAHAHAHAHAHAHAAHAHAHAHAHA*cough cough cough* LOZENGE!!"