I sympathise with your situation, Harry, but I'm not sure PPU are being totally honest with you. You can see what the different Interpol notices mean on their website here. If PPU say it's their duty to issue a green notice, they clearly don't think you're not a risk to anyone, no matter what they tell you to your face. They probably don't know where you can or can't go, as they almost certainly haven't tried to find out - they're happy to leave that to you and say the decisions are up to the destination countries. I'm sure our data is stored in line with the Data Protection Act, which has an exclusion for crime prevention.

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If you are to punish a man retributively you must injure him. If you are to reform him you must improve him. And men are not improved by injuries. (George Bernard Shaw)

Ultimately most countries don't ask about past convictions at all. It's mostly the English speaking countries- USA, Australia, Canada, New Zealand which will ask and they would most likely deny you entry. However when going to countries which don't ask, the only way those countries can find out is if your PPU have placed a green notice on your passport. So when they scan it your conviction details will show up and then they will most likely deny you entry. 

Travelling to the EU is another matter- you have the legal right to travel and even reside in any of the EU countries (whilst we're still in the EU). 

To be honest I have no idea what country filters out information on passports and that's the problem. Lie and you can be caught which is embarrassing, or don't delay it as they don't ask, then find that it comes to light at passport control.
The PPU know I am no risk to anyone so I am told by them that it is their duty to inform Interpol of my travel arrangements, as they did just weeks after I had visited my BF.
As for your other questions I want the answers to those as well. I really feel it is an injustice to not inform anyone with a criminal record as to where they can go and how our data is stored. 

I can't see anything on this site sorry

Within the EU, it is important to note that the grounds for preventing an EU citizen from entering another EU country - or for expelling them from another EU country - are extremely limited. A conviction, even for a serious crime, is not enough - the other country has to prove you pose a concrete threat.

So Germany, France, Portugal or any other country cannot deny you entry based on having a conviction. They would need evidence that you pose a present risk to public security in that country.

You can find more information on this in EU documentation for things like the Schengen Borders Code, Schengen Information System, and the EU's website on citizens' rights, which features sections on when an EU citizen can be denied entry to an EU country that they are not a citizen of.

One thing I found (from https://ec.europa.eu/citizensrights/front_end/docs/faq.pdf ):

Quote: As an EU citizen, you are free to enter and reside, subject to some conditions, in the other EU countries. This fundamental right of free movement can be restricted on grounds of public security, public health and public order. However, this restriction must be interpreted strictly, and it is only on grounds of present and serious threat to public security that you can be forbidden to enter another EU country. The mere existence of past convictions is not sufficient.

(End quote)

As an example, see this case involving an Italian citizen convicted of murder in the UK, whom the UK wanted to deport at the end of his sentence in UK prison. He challenged the deportation under EU freedom of movement rules, and won. The UK could not deport him as the murder he committed took place many years prior and he had not proven to be a present and serious threat.

https://www.theguardian.com/uk/2007/oct/31/humanrights.immigrationpolicy
https://news.bbc.co.uk/2/hi/uk_news/6958638.stm

I know USA and Australia are two countries you will never be allowed in
I reckon you would be OK with Germany and possibly France but i've never looked into it and i don't intend on traveling really.
I know for a fact Portugal is somewhere you can visit since i know of someone on the SOR who went there, however they did have family over there and they stayed with their parents, so it might depend on where you are staying and the purpose of your visit etc.
Visa's are probably a better way to ensure trouble free passage if one is granted. I certainly wouldn't just book a holiday on a whim and just expect to float through like regular people, i imagine calling the embassy for the respective country you intend to visit is a good port of call and obviously if you travel you have to let PPU know anyway. and by all accounts if you are traveling with other people and they don't know about your status and you get refused entry, well you will be in for a difficult time and some explaining to do in the most awkward time and place so i'd avoid that scenario.

Harry - its not that simple and you have to look at several variables.

1. Does the country allow entry simply because there are no visa requirements for a 'serious criminal offence' i.e. you don't have to lie on any form?
2. Does the country have an entry card / visa requirement to declare but would have no way of finding out if you were inclined to be less than truthful.
3. How does the PPU assess your risk and therefore the likelihood or otherwise that they will issue an Interpol green notice if you travel
4. If a green notice is issued, does the particular country check and update their own information systems or it just goes into a black hole
5. For low risk and no green notice issued, is your information still shared with the other country (e.g. FCC agreements or embassy to embassy)

To be fair, it's easy to get confused about the Marshall Islands, as they were administered by the USA after WW2, and the USA is still responsible for their defence. Their citizens can travel freely to the USA, including for work and study, but it doesn't look like they have to follow USA laws, including registration. Going back to the original list, I suspect many countries in SE Asia were motivated by high-profile publicity around certain individuals going there with the express purpose of offending. 

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If you are to punish a man retributively you must injure him. If you are to reform him you must improve him. And men are not improved by injuries. (George Bernard Shaw)

Thanks for that link. Interesting to see a US perspective, as ex-offenders over there suffer so much more than we do, with all their details being public and in some states being registered for life, regardless of the crime.

However, some of the details on their matrix are very inaccurate. It lists the Marshall Islands as being a US territory subject to US registration laws, when it's actually a completely independent country! Typically American geography genius, it treats "Africa" as a country, and it also states that Canada doesn't have a registry, when it does, it just isn't publicly available like in the US (it looks pretty similar to our system: https://www.rcmp-grc.gc.ca/to-ot/cpcmec-ccpede/bs-sc/nsor-rnds/index-eng.htm