Use your whole body to speak, not just your mouth.
Put your reading material on a shelf at eye level so you can read it while you are standing. Pull air into your lungs, and then push it out using your diaphragm and stomach. Breathe in this way as you read out loud. Imagine that you are an opera singer. Stand firm and try to reach the back of the room with your voice, without shouting or screaming, but just by using the power of your air supply and the vibration of your vocal flaps in your throat.
The goal is to put more power behind your sound. Speak slowly and enunciate each sound, each word. You can probably use the same paragraph over and over to practice controlling your breath, bringing it up from your diaphragm and taking care to pronounce each sound accurately.
Think of it as taking singing lessons, or going to the gym to build biceps. You must change your physical habits, your muscle memories, and create new ones for speaking. Singing lessons are a good analogy, because you must learn to take in deep breaths, control the air as it exits, and form the right shapes with your jaw, lips, and tongue.
Rather than speaking unconsciously, spend 15 minutes a day paying very close attention to exactly how you make the sounds of English and Russian. You can even try this–it works for my students: practice articulating the movements of the sounds of English, without making the sounds. Silently practice shaping the sounds as they should be made. If you don’t have a good source, go to http://soundsofspeech.uiowa.edu You’ll see interactive diagrams that show where your tongue should go, and how far down your jaw should lower. Practice those movements with making any sounds. Then try using your whole body and good breathing when you do start to pronounce the sounds and words.
Hope this helps!