Even though people have already addressed these, I like hearing myself talk (or read myself write...? Anyway...) I'll offer my two cents.
Large amounts of Orthodox theology/belief is passed on primarily through the experience of the liturgy and the prayers” what exactly do you mean? Do you mean like in the homily/sermon?
As was said, no. Actually, I do good to remember a sermon/homily from Sunday to Sunday. That's not good, I should, but it's not the main focus of the service, it is the Eucharist that is primary, and the liturgy in which it is accomplished. In the Liturgy, you find gems of theological depth such as the Justinian hymn:Only Begotten Son and Immortal Word of God,
Who for our salvation didst will to be incarnate of the holy Theotokos and ever virgin Mary,
Who without change didst become man and wast crucified, O Christ our God,
Trampling down death by death, Who art one of the Holy Trinity,
Glorified with the Father and the Holy Spirit, save us.
But I’d like to ask if Orthodox Christians can vote/believe as they please? I’m a leftie, you see, and I don’t really fit in with the Evangelicals or the Catholics because although I’m against abortion, I’m also against capital punishment, I’m anti–war, I think some socialist ideas are okay, and I don’t malign the president.
As was stated, The Orthodox Church isn't a political entity. You may vote how you wish. In the Southern US, you'll find many Orthodox are right-leaning (former evangelical converts, usually) but that's not so true in the North and Mid-West, or out in California (San Francisco has a sizeable Orthodox community, and is were the relics of St. John the Wonderworker of Shanghai and San Francisco reside).
Orthodoxy is open to those of any political leaning (I lean left myself, and would probably agree with all you said), but does not compromise on pro-life ethics, from conception until natural death. The Church opposes abortion, capital punishment, assisted suicide, etc. Even the Didache (ancient, possibly apostolic document of faith) has provisions against abortion. This is a shared opinion of the Orthodox Church and the Roman Catholic Church.
The Orthodox Church in America has consistantly held an anti-war opinion concerning the war in Iraq (IIRC, there were quite a few seminarians from St. Tikhon's that participated in anti-war rallies). The church is not dogmatically pacificistic, and has solemnly condoned war when all other options are exhausted in the past, but it is always with a heavy heart. "Just war theory" is not an Orthodox understanding. No war is just, but sometimes there is nothing else to be done in our fallen world. Historically, soliders who had killed in battle refrained from the Eucharist for three years (the penance for murder) to recognize the sinful nature of war.