off / on as prepositions

Off functions as a preposition of position or movement and is the converse of on. We speak of getting on a bus and off a bus, taking things off the table and putting them on the floor. In your first sentence, Tamas, off appears in off the coast to describe something that is situated near or next to land, but which is not exactly on the coast. Consider these other similar examples:

• We live just off The Avenue. Drive along The Avenue almost to the end and then turn off to the right into a little cul-de-sac.
• The Inner and Outer Hebrides are situated off the Western coast of Scotland.

Here are some examples of other common usages of off as a preposition:

• Did she jump off or fall off the cliff or did someone push her off? ~ Nobody knows!
• I'm off alcohol just now. A big celebration last Sunday. And it's put me off my food too.
• I think this crab pate has gone off, you know. It doesn't taste fresh any more.
• Have you heard? There's 20 % off all CDs at the music shop in Elm Street next Friday.
• You don't have to keep off the grass in this park. You can walk anywhere on the grass.

In your second sentence, Tamas, off describes time that is taken off work or off school typically because of illness, tiredness or holiday arrangements. Note that we do not need to say off from. One preposition, off, is enough here:

• We're getting two extra days off school at the beginning of June for the Queen's Jubilee.
• I shall have to have a day off soon. I can't keep going like this all the time.
  ~ Why don't you take the afternoon off today?
  

expresssions with off

We also speak about people being off-balance, off-colour, off-duty, doing things on the off-chance and having off days:

• I caught him completely off-balance and he didn't know what to say.
• She'd been off-colour for days, but there was no sign of any real illness developing.
• Could you just do this for me? ~ Sorry, love, I'm off duty at the moment. ~ When are you on again?
• I decided to take a detour into Paris on the off-chance that Amelie might be there.
• Brobbins, the club's leading striker, had an off day and missed three open goals.

phrasal verbs with off

There are many common phrasal verbs with off, such as put off (= postpone), knock off (finish work), lay off (dismiss from work, usually temporarily), bring something off (complete something successfully), polish off (eat something quickly):

• I've been putting it off for weeks, but it's no good, I shall have to go to the dentists soon.
• Aren't you going to knock off soon? You've been staring into that computer screen all day.
• 700 workers will be laid off in the Belfast shipyards following a decline in orders.
• They had a wonderful time. I didn't think you'd be able to bring it off.
• I thought the Christmas cake would hang around for weeks, but they soon polished it off.

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