First thing I'd say is that you need to educate yourself on all of this. These are some large $ amounts you are dealing with and I suggest you have a good understanding of what's going on. First, you should get a much better understanding of what the house is worth. Have the realtor walk you through how she came to her first price, and why it was decided to drop the price to $110k. You can get a good idea of what the house is worth simply by looking at comparable listings online. You can see what the houses are listed for and have recently sold for, then you can look at pictures to get an idea of what kind of shape they are in (redfin.com is a site I like to use). If the house needs work, you can just deduct the cost of those items from the price you come to based upon the Comparables. If you don't know how much the repairs are, you could always get estimates on them from a contractor. Have you gotten the house appraised? That's definitely an option that would be helpful.
Secondly, the property taxes owed are not just based on when some lawyer decides to foreclose on you. The rules are very rigid and straightforward. You need to know when the oldest taxes were due, then you can calculate when the county could put the house up for auction. And you can pay off the taxes on the house all the way up to the day of the auction (maybe even up to 2 years after the house is auctioned too, I believe). I'm sure a phone call to the County Tax Collector could get you all the information you need. The County would much prefer to get it's money than having to deal with auctioning the house, so it's in their best interest to help you understand the situation you are in. So make sure you understand the risk, or lack of risk, there.
Lastly, I don't know where you the house is (or where you are from), but houses in rural areas move much slower than they do in big cities. Just because it's been a few weeks and no one is interested doesn't mean that no one will be. Ask your realtor what the average listing time is on a house. I would venture to guess that it is more than 30 days. Don't panic and take a low ball offer from an investor just because it's been a few weeks.
Hopefully your realtor is helpful, but you should absolutely counter. You are never going to run an investor off because you came back high. 99 times out of 100 they will accept or counter. He may counter back at his original offer, but he will counter. Don't forget that this is what he deals with everyday and will try every trick he can to get the house for as cheap as possible. I'll repeat, don't panic and just accept a low offer because you are scared it won't sell. Remember, you are in possession of a huge asset: a house in a good school district. You will be able to get the deal that you are currently offered any day of the week, even the day before your house is up for auction. Think about it like this: the house is worth at least $130k when it's fixed up. I'm sure it needs some work, but unless you think it needs $50,000 of work (unlikely), then make sure you hold out for what it's actually worth.