The only way to truly and accurately parse address data is by using an online address validation service. The problem with addresses, and especially international addresses, is that there is no real standard. The other problem is that addresses are not "self validating" which means you can't tell if an address is good or even formatted properly by just looking at it. There are a few services out there that do address verification, and I believe there are a few that handle Israeli addresses.
Among those providers there are two basic ways to get your addresses cleaned. You can use their "batch scrubbing" capabilities where you upload a file and receive it back within a few minutes (or days), depending upon the provider. Or you could hook into their address verification web service API each time you receive an address. The correct answer depends upon your business needs and how immediate you need a response.
Most web service APIs will return the various component parts of an address--including street name--which allows you to perform your desired business function.
I should mention that I'm the founder of SmartyStreets. We do address verification for addresses in the United States. I realize you're trying to do Israeli addresses, but the domain knowledge I'm sharing here on the topic is generally universal in nature.