Is this a strong offer?

Depends on the asking price and what they were hoping for. If the agent/seller listed it very low to generate multiple offers, then $5K over is peanuts. If it's priced as market value and there's no other offers, that's a good offer.

It ultimately depends on what the actual market value of the home is.

Seems like a great deal to me! I would take it if i was the seller. If it gets declined you can always put in an offer of 275k and request a 3% seller concession that way you do not put too much out of pocket for closing costs.

To purchase this house, you should have income of $90000.

You show the seller that at $90K, you haven't saved.

Thus, you are a risk if the loan will ever get approved. 

Asking the seller to pay closing costs can make you look like a weak, borderline buyer with a strong risk of a lender turning you down, thereby tying up the seller's property for weeks and missing out on stronger buyers. In my area, once an offer is accepted with no other contingencies but the financing approval, that property is off the market and not shown anymore. If I was the listing agent, I would press the agent for the buyer on specifics about the buyer's finances, and advise my client based on that.

If you have the cash to pay the closing costs a buyer normally pays, pay them and don't complicate matters.There is also some degree of risk in the property not appraising for the higher amount, or being borderline. Lenders are not particularly crazy about financing closing costs, though there are some programs specifically for this.

depends on the market.   If the seller has multiple offers he may reject yours. If not, he may accept it.

In my area that would be a strong offer but in my area it's standard for the seller to pay closing costs; transfer tax and title insurance.

depends on the market where you are.

Your 'strong' offer doesn't matter if the agent or seller rejects it. The smart way to buy is to ask the agent if the seller would take an offer. That way the agent doesn't get irritated by your approach and he is more likely to promote your offer to the seller to effect a sale. Your blunt offer will likely just be used to lever more out of another buyer. 'Softly softly catchee monkey'.