I believe the question of when the Greeks turned Orthodox may have to be left for a religions-historian, but I feel that you have a few misconceptions about history that may make things more confusing than they really are.

At these old times there was no technology (tv,radio etc),so spreading propaganda was far more difficult than it is today

This is just partly true. It was different to spread propaganda back then, rather than harder. Statues, figurines, painted pottery, and so on, all worked very well for spreading propaganda.

Why did the greeks allow jews to convert them?As far as i know the jews never did religious wars unlike the muslims,so this means the jews used sneaky methods to spread their religion.

I'm not really sure where you are getting this from, but this statement is bordering on neo-nazism. Anyway, by the time the Greeks turned Christian they were an integral part of the Roman Empire. Therefore they simply followed the same path as the rest of the Empire after Constantine.

Was the immigration policy of ancient greece so weak?

Ancient Greece was not one country. Ancient Greece consisted of a thousand city states which all had their own different laws and citizens. Moving in and out of Greek city states as a free man wasn't all that hard, but you didn't have any rights. If you were to talk of an immigration policy it would be the time it would take to aquire citizenship after moving to a city state, apart from that it's a very modern concept.

was it so easy for jews to sneak into greece and to convert greeks and how did they achieve it?did they corrupt greek politicians?did jews ''capture'' important positions in the political hierarchy(mayors,presidents or something like that)?

This is just nonsense so it's a bit difficult to answer it properly. You're assuming that it was the Jews who turned the Greeks Christian, when it wasn't. There was no corruption (well, not related to this at least) and no capturing of mayors/presidents/what-have-you. The official conversion came as a direct result of the whole Roman state eventually converting from Paganism to Christianity.

I don't quite know where to start. Okay, let me say I have no interest in discussing modern Greece, the role of religion there, or anything of the sort.

"When did Greeks convert to Christianity?"

Roughly as a process between the middle of the 1st century (the 40s and 50s) through until the 5th century when an overwhelming majority would be Christians, at least nominally (it's meaningless to talk about nominalism in that context but we should at least acknowledge that perhaps some people were 'Christians' who didn't really mean it. I say it's meaningless because we can't measure anything like that, and you have to add layers of sociological and psychological interpretation to talk about).

Please keep in mind that in this period of history we are talking about the Eastern half of the Roman Empire, and the Greek city-states had varying degrees of autonomy within that, but overall not that much freedom. Secondly that this whole eastern half of the Mediterannean was 'Hellenised', i.e. dominated and influenced by Greek culture thanks to the legacy of Alexander the Great.

"How were the Greeks converted?"

Initially by transient missionaries such as Paul and others. Then, by the continued preaching/teaching/conversing of local Christian converts alongside other itinerant Christian figures. While those initial preachers are Jewish in background, most of the converting was done by Greeks themselves.

"Why did the Greeks allow Jews to convert them?"

Well, because they were persuaded and convinced that it was better for them to abandon their former religious practices and embrace this new religion. There was no force used in this period, and the social advantages on the whole seemed rather slim at least until the late 3rd and more the early 4th century. Now, the "why it was better for them" could be variously interpreted - some no doubt considered it true; others, that it offered something their own religious practices lacked; others, perhaps, because they did perceive social advantage on a micro or macro scale.

"Was the immigration policy of Ancient Greece so weak?"

Well, you can't really talk about an immigration policy. There was relatively free (in terms of restrictions) travel within the Empire at the time, and Paul himself was a Roman citizen already. Furthermore, as I said above, most of the converting was probably done by Greeks themselves.

"Did the Jews use sneaky methods?"

To be honest, the question is virtually racist. No, Jews did not 'sneak into Greece'. No, Jews did not corrupt Greek politicians. No, Jews did not use 'sneaky methods' to covertly operate and gain adherence for Christianity in Greece. Early participation in Christianity seems somewhat weighted towards lower classes, but there was a spectrum or cross-section of society. Personally, I find Edwin Judge's studies on early Christian social groupings and organisation to be particularly illuminating.