In U.S. practice,
A motion in limine is a motion seeking to rule on the admissibility of evidence at an evidentiary hearing or trial (usually a jury trial) in advance of the actual introduction of the evidence in order to allow greater certainty in trial preparation and a fuller legal explanation of the positions of the parties for the judge to consider than an oral objection and argument during a trial.
A motion to strike is a motion seeking removal of a document from consideration by a court because it has been filed improperly and possibly its removal from the court record entirely. It is provided for in the federal rules and most civil procedure rules based upon it in rule 12 where it is authorized to remove "redundant, immaterial, impertinent, or scandalous matter" be striken. For example, one might move to strike information revealing a trade secret that is attached to a court document, or the addition of an exhibit to a response to a motion to dismiss or motion for judgment on the pleadings that is supposed to be resolved based upon documents already filed only. Usually, a motion to strike wouldn't apply to trial evidence.
But, a motion to strike a jury demand, however, is really a motion to deny a request for a jury and not actually a request to remove the jury demand from a court file. But, the traditional name has struck.
- A motion to suppress would usually come up in a criminal case, asking that evidence illegally obtained by law enforcement not be presented as evidence in a case. This kind of motion to suppress is really a just sub-species of a motion in limine.
Another kind of motion to suppress, usually in a civil case, would be a motion seeking to limit who has access to a court file, usually out of privacy concerns.