Abarim Publications' online Biblical Greek Dictionary
None of the sources we commonly consult reports a connection between the following groups of words, but they are obviously similar in form and their meanings could be construed to overlap somewhat:
The adjective μυριος (murios) describes the greatest quantity expressible with a single word: innumerable, countless. It is also used to describe a definite number, which would be ten-thousand — not in the arithmetically accurate fashion of our English term "10,000", but rather a quantity of the order of ten thousand.
Our word is used in the New Testament only in the former sense of "a lot" (Matthew 18:24, 1 Corinthians 4:15 and 14:19 only) and is in that sense on a par with our modern idea of 'many millions' or 'billions and billions'. We moderns use bigger numbers to express the same idea of countlessness because we are used to larger numbers; 10,000 isn't that big to us but in the ancient world there weren't many occurrences of 10,000 of anything in everyday reality. Still, our English word "myriad" stems from this adjective.
A direct Greek derivation of our adjective is the noun μυριας (murias), which means the same, either a whole lot or else a quantity of the order of ten-thousand. This word is used 9 times in the New Testament; see full concordance.
The verb μυρω (muro) means to flow or trickle. This verb is used to describe mostly the flowing or tears and rivers and even blood. As such, this verb also came to be used in the sense of to weep for or bewail. This verb does not occur in the Bible.
The noun μυρον (muron) means ointment, or the costly oil-herb substance one may trickle or sprinkle on certain occasions (Matthew 26:7, Mark 14:3, John 11:2, Revelation 18:13). This costly muron was based on the mundane ελαιον (elaion), or olive oil, and the difference between the two is demonstrated by Jesus in Luke 7:46, where he says, "You have not anointed my head with elaion but she has anointed my feet with muron."
From μυρον (muron), meaning ointment, comes the verb μυριζω (murizo), meaning to anoint or sprinkle with muron, and in effect it means to make costly or mark as precious. This verb is used in the New Testament in Mark 14:8 only. Note that the anointing of Jesus' body had little to do with embalming — read our article on the name Nicodemus for the details.
How the Murex was lifted away
In classical times, preciousness and costliness went hand in hand with purple (πορφυρα, porphura). Royalty and nobility wore purple (Ezekiel 23:6, Daniel 5:7, Mark 15:17), and since time immemorial the Phoenicians were known for their production of it (Acts 16:14).
Purple dye was produced from small marine animals called Murex (murex, muricis), and although this name sounds decidedly Dr. Seussian, it's formally unclear where this name comes from.
Here at Abarim Publications we'd like to propose that the Murex was called such because (a) it expressed costliness, and (b) because a whole lot were needed for a small bit of dye (actually, it seems to us that the words for costliness, muchness and murex ultimately derive from the Semitic verb ארז, 'erez; see the name Meroz for the details).
Another noun of clear similarity is μυρος (muros), a kind of sea-eel (with an unguentous skin, perhaps?). This creature is not mentioned in the Bible but it is in the classics. It's not the same but named similarly as the μυραινα (muraina), the creature known in English as the Muraena or Moray eel.
This creature called μυρος (muros) was also known as σμυρος (smuros), which suggests relations between the word σμυρνα (smurna), meaning myrrh, and ultimately with the Semitic root מרר (marar), meaning to be strong or bitter.