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Knew these before those are both eligius nodes.Also how can I connect to RelayNetwork? What is their ip address? This 127.0.0.1?

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Some non-standard transactions can be pushed to network with
// https://blockchain.info/pushtx Relayed my non-standard tx's
// https://coinb.in/send-raw-transaction.html Didn't tried(have you?) but I will for sure try it.
// http://webbtc.com/relay_tx Didn't relayed them.
// http://eligius.st/~wizkid057/newstats/pushtxn.php (does not work right now) Well worked in past hope they will fix it.
// http://btc.blockr.io/tx/push Didn't relayed them.

I haven't checked these links for a long time.
Note: accepted != relayed
Note: relayed != mined

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Didn't really understood. Is there a command for bitcoind or something?

No. You should write your own tool which connects to a particular node, sends "mempool" command and analyses results. Wanna hire me?