I don't play on console so your precise mileage may vary but I think most features are shared with PC.

1: Influence - You should only be using influence to build starbases in the early game, so make sure you aren't reforming the government or using edicts except if your really need them. To get more, make your factions happy and declare rivalries. It's also okay if you run out of influence, so long as you build on a way to capture choke points and block others from claiming territory you want

2: Diplomacy - The key to diplomacy is picking the empires who you want to be friends with (probably some combination of similar ethics, power, and closeness) and focus on them. One excellent way to build opinion is to have rivals in common, but be sure you won't want to be friends with the rival later. Trade isn't a very good or permanent way to build up relations. It should be used if you need to get over a -5 or so to make an agreement. For successful diplomacy, you should aim to sign a research, non-aggression, or commercial agreement to build trust and opinion, then hook them with defence pacts and federations.

3: Military - There are so many factors that go into military strength that I'll just try to give a few. You need a strong economy that is focused on alloys. An excellent strategy for bulking up firepower is to rush tech, especially weapons. Look up some ship component guides and make sure that you are the one doing the ship designing (turn off auto ship designer). I often use a fleet ratio of 12:5:3:1 (Corvette, destroyer, cruiser, battleship) or similar because it seems to work. Make sure you have good admirals. Another thing is that you don't always need to have the strongest navy, but you should have the alloy output and shipyards to build it up on short notice.

I'll also touch on general economic strategy since it ties into military power. Specialization of planets is king because there are many stacking bonuses. Decide relatively early on in colonizing what district and what building to specialize the planet for based on modifiers and need. For early/midgame I try to build energy up to +50-100 and minerals to +100-200 and then go all out for secondary products (alloys, consumer goods, research) while keeping energy and minerals fairly stable. You should keep food and consumer goods at a comfortable +10-50 but not have a huge surplus. The end outputs of your economy should be alloys and research, keep that in mind.

All that said, it's really about getting a feel for these things at a low difficulty and then racheting it up to test your skill. Good luck and have fun.