I feel that my understanding of music theory is very poor.
When I play the piano, I really just ignore all the technicalities and various other things and just feel my way through the piece. Same with violin. I don't think I've ever learned to count while I play. It's just extremely difficult for me to concentrate on two or three things at once.
As a result, my sight-reading skills are very dismal. This is extremely crippling. I've realized this throughout all my years of musical experience, but I have never managed to rouse myself to do something about it.
I can read sheet music, to a point. It's very difficult for me to play a piece if I have never heard it before. I struggle with anything overtly complex, which is immensely embarrassing, considering how long I've been playing piano and violin. (I've been playing violin for around 7 years, since 5th grade. I've played piano for 2 years.)
The main reason why I have decided to invest my time into this, is that I realize that at a certain point, without the most instrumental understandings of music theory, my progression in my piano education will essentially plateau.
I do not think I can play more complex pieces entirely from ear reference.

Something that truly stumps me is the influence of a time signature on the speed of music. I believe the main reason why this is, is because I have never taught myself to count.
I cannot determine the speed of the piece simply from feeling, can I? What, for instance, is the difference between 3/4 and 6/8?

I'm a bit busy to answer all of your questions, but I'll answer your first:

The most efficient way to study music theory is to find yourself a teacher.

Right, I'm sensing three main areas here:

1. Most efficient way to study theory

2. Sight reading

3. Time/counting

I think firstly I will say that although they are interlinked, you should see them as separate issues- that way you can divide and conquer

1. Most efficient way to study theory

Forgive me if this ends up quite long, but I have a point to defend >.< For probably the first time ever I am going to disagree with Milchh, it's not something you need a teacher for at all unless you are looking at specialised practices such as Bach chorales/string trios etc.

The reason for this is that the majority of teachers who deal with amateurs are obsessed with graded examinations- mainly because they went through it themselves, because it's an established framework of music education and because they're too lazy to think outside the box. I think this slows down the process of learning and is essentially an indirect money making scam (if I ever get the money together to do a PhD, this will be the basis of my thesis so watch this space xD).

Anyway, less of that and let's talk about self study basic music theory. You do need a good reference book- this is your dictionary if you like. The best one we have in the UK is The AB Guide to Music Theory by Eric Taylor- you only need vol.1 for basic study. And it's cheap! Do not attempt to swallow this reference book, it's just for if you get stuck/need explanations. Then you need to grab a piece of music- literally anything but start small with solo works and build your way up- please don't attempt to begin with a Ravel orchestral score or something! It's quicker and easier for me to take you through it:

14833

I've taken a really basic example. I tell my students to consider the following areas: time signature + groupings, note values, clefs, intervals + key signature, performance directions. (Yes, I teach but I refuse point blank to prepare anyone for exams unless they need the piece of paper to move on in life).

Right, time signature C or 4/4, you can see that the notes are grouped in 4 of a kind- in cases where it doesn't add up to 4 they are grouped in 2 or 3. Note values- you say they are 4 of a kind but what kind? if you don't know you take out your reference book and find quavers and semiquavers. You see there are 2x4 semiquaver groups and 1x4 quaver group showing the relative values. If you like you can rewrite a couple of bars with other values of demisemi-semi or quaver-crotchet etc. You notice the effect this has on the speed of the music.

Clefs- we have treble and bass. If your note reading is rusty you can go along and name each note.

Intervals and key signature- this is where you may need a reference book to see it is in C major or A minor. How can we tell? Quickest initial way is to listen to it. Then when you hear it is C major you can go back to the notes and work out how it is C major which is where intervals come in- definitely good to have a reference book to get the hang of these. In the process of working out intervals, you notice a difference between the penultimate quaver of each bar and when listening/playing you notice the different sound this creates. I almost forgot that a really good exercise you can do with this is transposition. Take it to a keyboard and work it out in a few other keys, then you are indirectly learning about other keys too!

Performance directions- 'f' and the mordent above the quavers mentioned above. Also the dotted slurs if you like. These you need to look up and create a sort of log book to note them in as you come across them.

I think that's about it, but you see all of the things you can quite easily mine from two bars of actual music. It takes a little time and effort but because you have done it yourself you will have digested it and drawn your own conclusions rather than trying to decode how each theory textbook author/teacher explains it to you. Also, in theory textbooks, for every tiny thing I have mentioned above there are PAGES of exercises attempting to drill it into you, which if anything just make it quite boring.

I hope that makes some kind of sense and it did end up being long so I apologise. But trust me this method does produce results- I have gotten students passing grade 5 theory (the only essential theory qualification in the UK that you can't get onto most higher level music courses without) in a year when with normal teaching practices they take 5/6 because they also waste time and money taking grades 1-4. (I'm not contradicting myself by saying you can do it without a teacher- I don't teach my students theory, I have them do it a few times in lessons so I can see they've gotten the hang of the method and then I have them do it in their own time but bring proof to lessons.)

2. Sight reading

I really can't stress enough the importance of just keeping at it. There's nothing wrong with only being able to sight read if you've heard the piece of music first. This is the real world application of sight reading. Exam setting- who seriously grabs a piece of music they have never heard of and starts playing it? Yes back in the pre-recording days they had to do this, but move with the times. Listen to as much and as wide a range of music as possible. Anything you like, however simple or difficult, just get the music and sight read. Even if you just print out a page of the score and get to the end of the first line before giving up, you have achieved something.

Eventually this will develop into something you can do without having heard the piece of music, but the most efficient way of building up the mental facilities to do this is by starting simple and always listening to the piece of music first. Which bleeds into the final point:

3. Time/counting

Sit and listen to a clock ticking. You can probably tap along with it and accurately synchronise with the seconds after a few attempts. You wake up in the middle of the night and can tell it's the middle of the night. You naturally wake up at a certain time each morning. These are all examples of perception of time- the waking up examples are inbuilt, our circadian rhythms. The clock ticking is because we've all consciously and subconsciously heard it for years and years and years and instinctively know the rough duration of a second.

This is what you want to build up with music. The difference between 3/4 and 6/8? Initial answer would be a textbook one "3/4 is three crotchet beats per bar and 6/8 is two dotted crotchet beats per bar- the respective groupings are 3 groups of 2 and 2 groups of 3." Has that really answered your question? Doubtful. When playing or listening, the difference between the two of them is just something I feel- it's almost an instinct. Unless I'm playing something really rhythmically complex, I don't count when playing anymore. It wasn't always like that and I couldn't tell you how it became like that other than a result of living with music.

I would suggest doing a lot of listening work and counting along- without a score. Again, don't go and grab something like the Rite of Spring to start with- begin with things you already know like pop songs or something and you'll see that you already have some sort of grasp of how time works, even if you can't define or describe it. As you work on the above two areas, this is something that will become easier. Do a lot of clapping exercises- listen to things and clap back the rhythm, sit alone and do some impromptu rhythm tapping (I think all musicians do this anyway?)

That's my advice/thoughts. Hopefully others will have some more creative things you can do. That's the most important thing- be creative, it will come faster and more naturally if you make it enjoyable =]