OK, FIRST WALL OF TEXT INCOMING
@F0X
Firstly, if you're serious about wanting to enter the competitive Pokemon scene, I would start with reading this general overview by Smogon, which is generally regarded as the standard resource for competitive battling:
Introduction To Competitive Pokemon - Smogon University
I would also suggest using Smogon to look up any potential Pokemon you might want and read about team composition.
With that out of the way, let's get on to the Pokemon you currently have on your team! I'll be honest and say I haven't really dabbled in the X/Y Pokemon scene much; I kind of stopped in B&W. Because of this I don't know the most about gen 6 Pokemon and their place in the game, so most of the suggestions I'm giving you there are based on reading I've done. If there are any other folks here who do actively participate in sixth gen competitive battling, feel free to correct me!
Most of the Pokemon you currently have are either UU – underused – or OU – overused – so I'm going to be giving suggestions for an OU team. You can use UU/RU Pokemon in OU battles, though you might have a difficult time against teams that use strictly OU Pokemon. What I'm going to write is just preliminary impressions, before actually taking time to think about team composition and any potential additions (because I'm at work and shouldn't be doing this
at all whoops)
Delphox: Delphox appears to be RU – rarely used – and therefore might not be the strongest choice. However, it has a very high special attack stat, and has good resistances to a lot of common types. It also has pretty dang good special defense, and resists fighting, which is a good key to have! Unfortunately, you already have a psychic type in way of Gardevoir, and Gardevoir is simply better in all ways. Fire isn't the most desirable type to have, due to the prevalence of stealth rock.
Lucario: Lucario is super powerful; Mega Lucario can even be used in Uber battles despite not being a legendary Pokemon. However, regular Lucario can be used in both OU and UU tiers, so as long as you don't want him to be mega, you're all right. He's a solid physical sweeper with a decent bit of utility. Just a good pick all around.
Gardevoir: You might want to consider making Gardevoir your mega. Mega Gardevoir is a hard hitting special attacker and, more importantly, a wallbreaker – meaning it's good at tanking down walls (which I'll get more into with Umbreon.) It has decent speed, but not high enough to save it from some potent revenge killers. Pixilate is also an incredible ability to have, making Hyper Voice chunk most Pokemon that don't resist Fairy.
Umbreon: Umbreon is what you call a wall – what other games might call a 'tank.' It has really good defensive stats, with its special defense being slightly higher than its defense. It's also a baton passer, meaning that it 'sets up' for other Pokemon on your team. Its standard trick is Wish + Baton Pass, which allows your other Pokemon to take advantage of Wish's heal. Umbreon is just a really solid pick, so definitely keep it on your team!
So as it stands, you have a super strong physical sweeper (Lucario) who has good access to steel and fighting stats, and has decent resistances. You also have a good wall in the way of Umbreon, and a good, albeit slightly slow, special attacker in the way of Gardevoir. Delphox is kind of sticking out like a sore thumb here, so you have to ask yourself if it's a Pokemon you really, really want to keep, in which case you might have to replace Gardevoir with something else. That's up to you. You're also lacking someone who can set up hazards (stealth rock, toxic spikes) and a speedy revenge killer, ideally. As mentioned, I haven't quite done any thinking as to who else I can add and what kind of team composition you might like! First I wanna ask who you'd rather keep: Gardevoir or Delphox.
Edit: Also, come to think of it, Swampert might be a good addition! He's tanky and has access to Stealth Rock, and his ground typing gives him super utility.