You obviously want both to address both issues you mention, getting people to buy or rent, and getting people to rent out/sell their property but I'm going with getting the properties listed in the first place is your bigger issue.
You have hit upon the big estate agent (realtor in North America?) issue that I have seen in the UK; getting the properties onto the site in the first place.
You are in a very competitve market and competing against the big realtors with, presumably, good marketing budgets; so, short term, unless you are very lucky SEO will be a real struggle; especially if you can't identify the real convertable search terms.
Having said that, for the traffic (SEO or SEM) you do get, I would suggest that you have a form on your site's pages (all of them) saying something like 'What is your house worth?' or 'how much could you rent your house for?' then get them to complete email/phone and say you'll call back.
This may get those who visit your site to buy or rent to consider using you for selling or renting their existing property.
Then, go and see if you can talk to some people who are selling/renting through the local competition and ask them how they chose to use whoever they did. Web?, press advertising?, other?... this may give you some good ideas how to offline market to others, and help your online marketing ideas, especially for keyphrases. You could also perhaps do this in the form of a 'survey' (if you are braver then me!); 'if you were going to rent out your house, how would you choose who to advertise it with?', then follow up questions depending upon answer.
Email marketing I think will need many hundreds of thousands sent out to get any reasonable response; I don't favour it personally, but can work occasionally.
The rule of thumb for leaflet drops (postcards in your case) etc that I was taught was 1% of 1% - if the leaflet drop was untargetted then 1% may be interested and of those 1% will do business. Now for you, sending only to those who you KNOW want to sell/rent anyway you can probably just go with 1% (not sure how that % matches your experience) - from this you can get some idea of the spend and reach you need to be making to get your target numbers.
Working on the local angle may be the way to go to start with; rather that trying to be all things to all people, try to get the local angle going first - so then you can try to get interviews with local press about how, in these difficult times, you are offering a new, more economical way for people to sell/rent their homes, and as a new business you are hoping to expand and employ x people over the next 2 to 3 years as the business expands (ie PR); you could also look at spending some money on the local press advertising in the property sections... start building a brand locally, then put so much money aside each month to start an advertising fund as you spread your net wider.
Going local will also let you better target your SEM and SEO and face less competition. You can always have the Global forsobo.com, but then have region specific sites forsobo.com/michegan/chester etc.. (As a side point, looking at your site I have no idea where the properties are; Chester but where is Chester? - making me click on properties to even find out if I'm in the right county/state isn't great IMO - also, your search isn't prominent enough for me - and is lost competely on the property detail pages, I would look to move it to the menu bar somewhere - also, also,
the examples in the search are for type of house; where I do search for town or an area?)
Very long, but I hope is more help than hinderance