Incorporating fruits in creme brulee

This is a tough question. Fresh fruit puree is very unsuitable for incorporating in custards if you want a strong flavor. It contains tons of water, and dilutes your creme brulee a lot, and also brings the pH balance out of whack, interfering with the setting. You can only incorporate small amounts for color and a hint of flavor. Don't forget to add sugar to the puree when you are doing this, it strengthens the fruit flavor perception and reduces the negative effects on texture.

If you want a strong flavor, here are your options when having access to normal kitchen equipment, in order of closeness to the ideal of getting real strawberry flavor into otherwise typically-textured creme brulee:

1. Purchase strawberry aroma and use it. Don't forget to color the creme brulee, either with food coloring or with small amounts of puree.
2. Use freeze dried strawberry powder. You might have difficulty finding the real thing (pure strawberry juice freeze-dried) as opposed to maltodextrin-based powders, read the description carefully. An alternative is to grind strawberries which you have dehydrated yourself, but that will give you inferior results.
3. Cook down your own strawberry simple syrup and use that. This works with any fruit. Start with pressing juice of an amount roughly equal to your dairy base - if your recipe uses 350 ml of cream and 150 ml of milk, you need 500 ml of strawberry juice. Depending on your juicer, this will need 1.5 - 2 kg of strawberries. Make the juice, then add sugar at 1:3 ratio (so 165 g sugar for 500 g of juice). Cook on a low flame until a candy thermometer shows 104 Celsius. Let it cool to room temperature before using in the creme brulee. Quick alternative with somewhat worse taste: use a store bought jam, preferably a smooth spread without chunks.
4. Use liqueur. This is usually done with other fruits where there are traditional brands of liqueur, such as cassis, grand marnier or frangelico. But if you can find a good strawberry liqueur, try that. Alcohol is a great flavor carrier and will give you aromas you can't get from cooked down or dehydrated fruit. For best results, combine the alcohol with one of the other solutions here.
5. Instead of putting the flavor agent within the custard, go the traditional route and pour a fruit sauce over it. You can use the reduction from the previous point for that, or make it in some other way.
6. Again, instead of flavoring the custard itself, pour it over whole strawberries in the mold. This works better with poured custards or puddings rather than creme brulee, since the strawberries won't take kindly to baking.
7. Instead of making creme brulee, make a strawberry sabayon, using fruit puree or fruit juice as the liquid to be thickened by the yolks. This dessert has a strong fruity flavor, but a very different texture, and it also brings out the egginess of the egg yolks.

As an aside, these methods are useful beyond creme brulee, you have the same options for all creamy desserts (including panna cotas, starch puddings, cheese based cremes) and many types of cake icing, especially buttercreams.

I've successfully cooked Creme Brulée with whole raspberries at the bottom. Perhaps you could use a similar strategy, e.g. put in halved strawberries (perhaps with the cut face against the bottom of the bowl to minimise interaction). Whole fruit will minimise altering the pH or water content provided it doesn't disintegrate. You could combine this with some strawberry aroma in the custard itself.

My favourite solution to the problem is to infuse the cream with a Strawberry (or any flavour) tea (well technically infusion)

Here is the one I used but I suspect any would do. Just infuse overnight in the fridge and then strain after you have heated the cream .

Try an approach that often is used when making posset! First, cook cream and sugar (similar measurements as in a creme brulee), then pour a spoonful or two of the cream-sugar mixture into the strawberry pure and stir thoroughly. This should neutralize a fair share of the acidity that causes splitting. Then pour the strawberry puree in the cream, and stir thoroughly.

You could possibly whip the egg yolks separately with some sugar to help you obtain the desired texture, then slowly incorporate the cream into the yolks and then go on as usual with the creme brulee.

I am not promising anything, but this might work?