The word that is translated "miracle" is typically the word "dunamis." Vines defines it as, "...power, inherent ability, is used of works of a supernatural origin and character, such as could not be produced by natural agents and means." You will also find this word translated as "power" throughout the New Testament. When "miracle" is used for the translation, it is when a specific occurrence is being referenced, one that necessitated power of supernatural origin (see Matthew 7:22). If you want to see examples of where "dunamis" is translated "power" then see Mark 5:30 and Ephesians 1:19.
New Ungers Bible Dictionary has a great definition for miracles, "supernatural manifestations of divine power in the external world, in themselves special revelations of the presence and power of God."
"Wonders" is the typically a translation for "teras" which according to The Complete Word Study New Testament, "to watch, as that which for its extraordinary character is apt to be observed and kept in memory." You can find this word in Matthew 24:24 and Acts 4:30. The word "miracle" is the more general word, a category of sorts, in which "wonders" could be thought of as a subset. Not every miracle is a wonder but every wonder is a miracle. An example of a miraculous wonder is when we practice tithing, priority percentage giving, we have less according to the math but for everyone who faithfully does this, you know, we always end up with more! It is a miraculous wonder!
"Signs" is from the word "semeion" which according to TCWSNT, "valuable not so much for what they are as for what they indicate of the grace and power of the doer or his/her immediate connection with God." When you read Mark 16:20, Acts 14:3, and Hebrews 2:4, you will see how "signs" has a special meaning relative to the others although it often appears in a list with them. Again, not every miracle is a sign but every sign is a miracle. An example of a miraculous sign is Jesus' virgin birth. A miracle most certainly but more importantly, a sign for Jesus being the Messiah!
In Acts 2:37 we see a great example of a miraculous wonder in that Peter's sermon was just words, but words that were supernaturally empowered from on high, words that "...pierced to the heart..." and brought the listeners to a moment of surrender to God!
In Acts 2:25-28 we see a great example of a miraculous sign through the prophecy that David gave centuries before in speaking of the Messiah in Psalm 16:8-11.
May we be a people of miracles, wonders, and signs!!